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On the computation and inversion of the cumulative noncentral beta distribution functionMay 17 2019The computation and inversion of the noncentral beta distribution $B_{p,q}(x,y)$ (or the noncentral $F$-distribution, a particular case of $B_{p,q}(x,y)$) play an important role in different applications. In this paper we study the stability of recursions ... More

Solution to the Stieltjes moment problem in Gelfand-Shilov spacesMay 17 2019We characterize the surjectivity and the existence of a continuous linear right inverse of the Stieltjes moment mapping on Gelfand-Shilov spaces, both of Beurling and Roumieu type, in terms of their defining weight sequence. As a corollary, we obtain ... More

On a generalized class of boundary-value problems with delayed argumentMay 17 2019In this work, spectrum and asymptotics of eigenfunctions of a generalized class of boundary value problems with a delay are obtained.

Fourier frames for surface-carried measuresMay 16 2019In this paper we show that the surface measure on the boundary of a convex body of everywhere positive Gaussian curvature does not admit a Fourier frame. This answers a question proposed by Lev and provides the first example of a uniformly distributed ... More

Norm Inequalities for the Fourier Coefficients of Some Almost Periodic FunctionsMay 16 2019Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to prove norm inequalities for Besicovitch almost periodic functions. This yields an analogue of Paley's Inequality for the Fourier ... More

A complex analysis approach to Atangana-Baleanu fractional calculusMay 16 2019The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can be rewritten as a complex contour integral which can be used to provide ... More

Distributions with Decay and Restriction ProblemsMay 16 2019In this paper we introduce a new type of restriction problem, called the \textit{restriction problem with moments}. We show that the surface area measure of the sphere satisfies the $L^p$-$L^2$ restriction problem with moments if $1 \leq p < \frac{2(d+2)}{d+3}$ ... More

Sherman's inequality and its converse for strongly convex functions with applications to generalized f-divergencesMay 16 2019Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using extended idea ... More

Random discretization of O'Hara knot energyMay 16 2019We considered random discrete approximation of O'Hara energy. O'Hara energy is the energy defined for a knot, and O'Hara energy was introduced for defining the standard shape for each knot class (equivalence class by ambient isotopy) by variational method. ... More

Stability criteria for second order linear ordinary differential equationsMay 16 2019We use some properties of solutions of Riccati equation for establishing boundedness and stability criteria for solutions of second order linear ordinary differential equations. We show that the conditions on coefficients of the equations, appearing in ... More

Weak endpoint bounds for matrix weightsMay 15 2019We prove quantitative matrix weighted endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class $A_1$ introduced ... More

Geometric Polynomials: Properties and Applications to Series with Zeta ValuesMay 15 2019We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

Jacob's ladders and infinite set of transmutations of asymptotic complete hybrid formula on level curves in Gauss' planeMay 15 2019In this paper we have obtained new phenomenon lying in the following: every fixed asymptotic complete hybrid formula (we call it as mother formula) generates infinite set of new formulas (transmutations) such that every new formula expresses a close binding ... More

Fractional damping through restricted calculus of variationsMay 14 2019We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton's principle. Fractional damping is a particular instance of non-local (in time) damping, ... More

A discrete approach to Wirtinger's inequalityMay 14 2019Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's ... More

Morse index and stability of the planar N-vortex problemMay 13 2019This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical ... More

Oscillation of Functions in the Hölder classMay 13 2019We study the size of the set of points where the $\alpha$-divided difference of a function in the H\"older class $\Lambda_\alpha$ is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated ... More

Orthogonal Polynomials, Asymptotics and Heun EquationsMay 13 2019The Painlev\'{e} equations arise from the study of Hankel determinants generated by moment matrices, whose weights are expressed as the product of ``classical" weights multiplied by suitable ``deformation factors", usually dependent on a ``time variable'' ... More

The capacity of quiver representations and Brascamp-Lieb constantsMay 12 2019Let $Q$ be a bipartite quiver, $V$ a real representation of $Q$, and $\sigma$ an integral weight of $Q$ orthogonal to the dimension vector of $V$. In this paper, we introduce the Brascamp-Lieb operator $T_{V,\sigma}$ associated to $(V,\sigma)$ and study ... More

High-order derivatives of the Bessel functions with an applicationMay 12 2019We determine the asymptotic behaviour of the $n$th derivatives of the Bessel functions $J_\nu(a)$ and $K_\nu(a)$, where $a$ is a fixed positive quantity, as $n\to\infty$. These results are applied to the asymptotic evaluation of two incomplete Laplace ... More

High multiplicity and chaos for an indefinite problem arising from genetic modelsMay 12 2019We deal with the periodic boundary value problem associated with the parameter-dependent second-order nonlinear differential equation \begin{equation*} u'' + cu' + \bigr{(} \lambda a^{+}(x) - \mu a^{-}(x) \bigr{)} g(u) = 0, \end{equation*} where $\lambda,\mu>0$ ... More

Wellposedness of the discontinuous ODE associated with two-phase flowsMay 11 2019We consider the initial value problem \[ \dot x (t) = v(t,x(t)) \;\mbox{ for } t\in (a,b), \;\; x(t_0)=x_0 \] which determines the pathlines of a two-phase flow, i.e.\ $v=v(t,x)$ is a given velocity field of the type \[ v(t,x)= \begin{cases} v^+(t,x) ... More

An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0May 11 2019The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;\gamma^2)$ of order $0$, bandlimit $\gamma > 0$ and characteristic exponent $n$ has running time which grows with both $n$ and ... More

Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomialsMay 10 2019Let $\displaystyle \{x_{k,n-1}\} _{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\} _{k=1}^{n},$ $n \in \mathbb{N}$, be two sets of real, distinct points satisfying the interlacing property $ x_{i,n}<x_{i,n-1}< x_{i+1,n}, \, \, \, i = 1,2,\dots,n-1.$ Wendroff ... More

A new perspective on the distance problem over prime fieldsMay 10 2019Let $\mathbb{F}_p$ be a prime field, and ${\mathcal E}$ a set in $\mathbb{F}_p^2$. Let $\Delta({\mathcal E})=\{||x-y||: x,y \in {\mathcal E} \}$, the distance set of ${\mathcal E}$. In this paper, we provide a quantitative connection between the distance ... More

Nielsen's beta function and some infinitely divisible distributionsMay 10 2019We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form ... More

Phase retrieval for wide-band signalsMay 10 2019This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x|} dx), we find all functions g $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x| ... More

Hardy spaces on homogeneous groups and Littlewood-Paley functionsMay 10 2019We establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood-Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.

Some relations following from the decomposition formula for one multidimensional Lauricella hypergeometric functionMay 10 2019Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients were constructed recently. These fundamental solutions are directly connected with multiple Lauricella hypergeometric function and the decomposition ... More

$L^\infty$-$BMO$ bounds for pseudo-multipliers associated to the harmonic oscillatorMay 09 2019In this note we will investigate some conditions of H\"ormander-Mihlin type in order to assure the $L^\infty$-${BMO}$ boundedness for Hermite pseudo-multipliers. The $H^1$-$L^1$ continuity for multipliers of the harmonic oscillator also is investigated. ... More

On point-mass Riesz external fields on the real axisMay 09 2019The purpose of this work is twofold. First, we aim to extend for $0<s<1$ the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials ($s=0$). Our ... More

A Trace Theorem For Sobolev Spaces On The Sierpinski GasketMay 08 2019We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain ... More

A Henstock-Kurzweil type integral on 1 dimensional integral currentsMay 08 2019We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem of Calculus ... More

Efficient Algorithms for Approximate Smooth SelectionMay 08 2019In this paper we provide efficient algorithms for approximate $\mathcal{C}^m(\mathbb{R}^n, \mathbb{R}^D)-$selection. In particular, given a set $E$, constants $M_0 > 0$ and $0 <\tau \leq \tau_{\max}$, and convex sets $K(x) \subset \mathbb{R}^D$ for $x ... More

The Fourier transform on harmonic manifolds of purely exponential volume growthMay 08 2019Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except for the flat ... More

Boundedness properties of maximal operators on Lorentz spaces in non-doubling settingMay 08 2019We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces $L^{p,q}(\mathfrak{X})$ in the context of certain non-doubling metric measure spaces $\mathfrak{X}$. The special class of spaces for ... More

A Dimension-Free Hermite-Hadamard Inequality via Gradient Estimates for the Torsion FunctionMay 08 2019Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a subharmonic function, $\Delta f \geq 0$, which satisfies $f \geq 0$ on the boundary $\partial \Omega$. Then $$ \int_{\Omega}{f ~dx} \leq |\Omega|^{\frac{1}{n}} ... More

Discrete Fractional Integration Operators Along the PrimesMay 07 2019We prove that the discrete fractional integration operators along the primes \[ T^{\lambda}_{\mathbb{P}}f(x) := \sum_{p} \frac{f(x-p)}{p^{\lambda}} \cdot \log p \] are bounded $\ell^p\to \ell^{p'}$ whenever $ \frac{1}{p'} < \frac{1}{p} - (1-\lambda), ... More

Remarks on some properties of special polynomials with exponential distributionMay 07 2019In this notice, we revisit the recent work [1] of Jung Yoog Kang and Tai Sup about special polynomials with exponential distribution in order to state some improvements and get new proofs for results therein.

Differentiating along rectangles with fixed shapes in a set of directionsMay 07 2019In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to the basis, the ratio of the largest of its side-lengths ... More

On metrics of constant positive curvature with four conic singularities on the sphereMay 07 2019We show that for given four points on the sphere and prescribed angles at these points, which are not multiples of $2\pi$, the number of metrics of curvature 1 having conic singularities with these angles at these points is finite.

Optimal partitioning of an interval and applications to Sturm-Liouville eigenvaluesMay 07 2019We study the optimal partitioning of a (possibly unbounded) interval of the real line into $n$ subintervals in order to minimize the maximum of certain set-functions, under rather general assumptions such as continuity, monotonicity, and a Radon-Nikodym ... More

Multilinear singular integrals on non-commutative $L^p$ spacesMay 06 2019We prove $L^p$ bounds for the extensions of standard multilinear Calder\'on-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mean the pointwise product in UMD function lattices, or the composition ... More

Improved asymptotics for the Ablowitz-Segur solutions of the inhomogeneous Painlevé II equationMay 06 2019We study the asymptotic behavior of solutions for the second Painlev\'e equation using the Riemann-Hilbert approach and steepest descent analysis. The solution of a Riemann-Hilbert problem related to the Painlev\'e II equation can be represented by means ... More

Locally $C^{1,1}$ convex extensions of $1$-jetsMay 06 2019Let $E$ be an arbitrary subset of $\mathbb{R}^n$, and $f:E\to\mathbb{R}$, $G:E\to\mathbb{R}^n$ be given functions. We provide necessary and sufficient conditions for the existence of a convex function $F\in C^{1,1}_{\textrm{loc}}(\mathbb{R}^n)$ such that ... More

Locally $C^{1,1}$ convex extensions of $1$-jetsMay 06 2019May 15 2019Let $E$ be an arbitrary subset of $\mathbb{R}^n$, and $f:E\to\mathbb{R}$, $G:E\to\mathbb{R}^n$ be given functions. We provide necessary and sufficient conditions for the existence of a convex function $F\in C^{1,1}_{\textrm{loc}}(\mathbb{R}^n)$ such that ... More

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces I: Decompositions with Applications to Boundedness of Calderón--Zygmund OperatorsMay 06 2019Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered Hardy--Littlewood ... More

Multivariate Bernoulli polynomialsMay 06 2019We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties : difference and differential relations, symmetry, explicit formula, multiplication theorem, and binomial type formula. Further, we consider a multivariate ... More

Supercritical Moser-Trudinger inequalities and related elliptic problemsMay 06 2019Given $\alpha >0$, we establish the following two supercritical Moser-Trudinger inequalities \[ \sup\limits_{u \in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\big( (\alpha_n + |x|^\alpha) |u|^{\frac{n}{n-1}} \big) dx < +\infty ... More

A supercritical Sobolev type inequality in higher order Sobolev spaces and related higher order elliptic problemsMay 06 2019A Sobolev type embedding for radially symmetric functions on the unit ball $B$ in $\mathbb R^n$, $n\geq 3$, into the variable exponent Lebesgue space $L_{2^\star + |x|^\alpha} (B)$, $2^\star = 2n/(n-2)$, $\alpha>0$, is known due to J.M. do \'O, B. Ruf, ... More

On Descartes' rule of signsMay 06 2019A sequence of $d+1$ signs $+$ and $-$ beginning with a $+$ is called a {\em sign pattern (SP)}. We say that the real polynomial $P:=x^d+\sum _{j=0}^{d-1}a_jx^j$, $a_j\neq 0$, defines the SP $\sigma :=(+$,sgn$(a_{d-1})$, $\ldots$, sgn$(a_0))$. By Descartes' ... More

Improvement and generalization of some Jensen-Mercer-type inequalitiesMay 06 2019The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.

Wild examples of rectifiable setsMay 05 2019We study the geometry of sets based on the behavior of the Jones function, $J_{E}(x) = \int_{0}^{1} \beta_{E;2}^{1}(x,r)^{2} \frac{dr}{r}$. We construct two examples of countably $1$-rectifiable sets in $\mathbb{R}^{2}$ with positive and finite $\mathcal{H}^1$-measure ... More

Analytic solution for one dimensional inverse heat conduction problem of semi-infinite barMay 04 2019We present analytical formula along with its existence theorem for solution of inverse heat conduction problem of semi-infinite bar, equivalent to a Volterra integral equation of first kind, as an infinite series of fractional derivatives. The mathematical ... More

Oscillation properties of one boundary problem of fourth order with a spectral parameter in the boundary conditionsMay 04 2019For one boundary problem of fourth order with a spectral parameter in the boundary condition we prove the simplicity of the spectrum and the oscillation properties of the system of the eigenfunctions derivatives.

Weighted Estimates of Singular Integrals and Commutators in the Zygmund Dilation SettingMay 03 2019The main purpose of this paper is to establish weighted estimates for singular integrals associated with Zygmund dilations via a discrete Littlewood--Paley theory, and then apply it to obtain the upper bound of the norm of commutators of such singular ... More

Modified Riemann sums of Riemann-Stieltjes integrable functionsMay 02 2019In this paper, motivated by physical considerations, we introduce the notion of modified Riemann sums of Riemann-Stieltjes integrable functions, show that they converge, and compute them explicitely under various assumptions.

Generalizations of Menchov-Rademacher theorem and existence of wave operators in Schrodinger evolutionMay 01 2019We obtain generalizations of the classical Menchov-Rademacher theorem to the case of continuous orthogonal systems. These results are applied to show the existence of Moller wave operators in Schrodinger evolution.

Nikolskii inequality for lacunary spherical polynomialsMay 01 2019We prove that for $d\ge 2$, the asymptotic order of the usual Nikolskii inequality on $\mathbb{S}^d$ (also known as the reverse H\"{o}lder's inequality) can be significantly improved in many cases, for lacunary spherical polynomials of the form $f=\sum_{j=0}^m ... More

Lauricella's $F_C$ with finite irreducible monodromy groupMay 01 2019We study the conditions under which the monodromy group for Lauricella's hypergeometric function $F_C (a,b,c;x)$ is finite irreducible. We give the conditions in terms of the parameters $a,b,c$.

Quantitative Comparisons of Multiscale Geometric PropertiesApr 30 2019We generalize some characterizations of uniformly rectifiable (UR) sets to sets whose Hausdorff content is lower regular (and in particular, do not need to be Ahlfors regular). For example, David and Semmes showed that, given an Ahlfors $d$-regular set ... More

Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic formApr 30 2019May 06 2019There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions ... More

Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic formApr 30 2019There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions ... More

Asymptotics of a sum of modified Bessel functions with non-linear argumentApr 30 2019We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \[S_{\nu,p}(a)=\sum_{n\geq 1} (an^p/2)^{-\nu} K_\nu(an^p)\qquad (a>0,\ 0\leq\nu<1)\] as the parameter $a\to 0+$, where $p$ denotes an ... More

The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processesApr 30 2019We evaluate the sum of Gauss hypergeometric functions \[S(\mu,c;x)=\sum_{k\geq 0} \bl(\frac{1-x}{1+\mu}\br)^k\,{}_2F_1(k/2+1/2, k/2+1;c;x)\] for $x\in [-1,1]$ and positive parameters $\mu$ and $c$. The domain of absolute convergence of this series is ... More

Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domainsApr 30 2019In relatively nice geometric settings, in particular, on Lipschitz domains, absolute continuity of elliptic measure with respect to the Lebesgue measure is equivalent to Carleson measure estimates for solutions, to square function estimates, to $\varepsilon$-approximability, ... More

On the equality of Bajraktarević means to quasi-arithmetic meansApr 29 2019This paper offers a solution of the functional equation $$ \big(tf(x)+(1-t)f(y)\big)\varphi(tx+(1-t)y)=tf(x)\varphi(x)+(1-t)f(y)\varphi(y) \qquad(x,y\in I), $$ where $t\in\,]0,1[\,$ is a fixed number, $\varphi:I\to\mathbb{R}$ is strictly monotone, and ... More

A simultaneous version of Host's equidistribution TheoremApr 29 2019Let $\mu$ be a probability measure on $\mathbb{R}/\mathbb{Z}$ that is ergodic under the $\times p$ map, with positive entropy. In 1995, Host showed that if $\gcd(m,p)=1$ then $\mu$ almost every point is normal in base $m$. In 2001, Lindenstrauss showed ... More

On Hyperbolic Polynomials and Four-term Recurrence with Linear CoefficientsApr 29 2019For any real numbers $a,\ b$, and $c$, we form the sequence of polynomials $\{P_n(z)\}_{n=0}^\infty$ satisfying the four-term recurrence \[ P_n(z)+azP_{n-1}(z)+bP_{n-2}(z)+czP_{n-3}(z)=0,\ n\in\mathbb{N}, \] with the initial conditions $P_0(z)=1$ and ... More

On Lebesgue null setsApr 28 2019Letting A be a Borel subset of n dimensional Euclidean space, and W(x) be an m dimensional affine subspace containing x and varying in a Lipschitz way according to x, we establish that A is Lebesgue null if and only if $A \cap W(x)$ has m dimensional ... More

The Fuglede conjecture for convex domains is true in all dimensionsApr 28 2019Let $\Omega$ be a convex body in $\mathbb{R}^d$. We say that $\Omega$ is spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. There is a conjecture going back to Fuglede (1974) which states that $\Omega$ is spectral if ... More

On sets in ${\mathbb R}^d$ with DC distance functionApr 27 2019We study closed sets $F \subset {\mathbb R}^d$ whose distance function $d_F:= {\rm dist}\,(\cdot,F)$ is DC (i.e., is the difference of two convex functions on ${\mathbb R}^d$). Our main result asserts that if $F \subset {\mathbb R}^2$ is a graph of a ... More

On double q-Laplace transform and applicationsApr 27 2019We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.

Discrete semiclassical orthogonal polynomials of class 2Apr 26 2019In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit relations between ... More

Fourier multipliers on a vector-valued function spaceApr 26 2019In this work we will study a vector-valued version of Hormander's multiplier theorem. Our result improves the result of Triebel and extends to the case p=infinity in the scale of Triebel-Lizorkin space.

Representation of the Mittag-Leffler function through the exponential functions in the case of rational derivativesApr 26 2019In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous papers the given ... More

A counterexample to Fuglede's conjecture in $(\mathbb{Z}/p\mathbb{Z})^4$ for all odd primesApr 25 2019In this short note we construct a spectral, non-tiling set of size $2p$ in $(\mathbb{Z}/p\mathbb{Z})^4$, $p$ odd prime. This example complements a previous counterexample in [arXiv:1509.01090], which existed only for $p \equiv 3 \pmod{4}$. On the contrary ... More

A counterexample to Fuglede's conjecture in $(\mathbb{Z}/p\mathbb{Z})^4$ for all odd primesApr 25 2019Apr 29 2019In this short note we construct a spectral, non-tiling set of size $2p$ in $(\mathbb{Z}/p\mathbb{Z})^4$, $p$ odd prime. This example complements a previous counterexample in [arXiv:1509.01090], which existed only for $p \equiv 3 \pmod{4}$. On the contrary ... More

A semicircle law and decorrelation phenomena for iterated Kolmogorov loopsApr 25 2019We consider a standard one-dimensional Brownian motion on the time interval $[0,1]$ conditioned to have vanishing iterated time integrals up to order $N$. We show that the resulting processes can be expressed explicitly in terms of shifted Legendre polynomials ... More

Uncertainty principles for eventually constant sign bandlimited functionsApr 25 2019We study the uncertainty principles related to the generalized Logan problem in $\mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $m\in \mathbb{Z}_{+}$, find \[ \sup\{|x|\colon (-1)^{m}f(x)>0\}\cdot ... More

Classical Kantorovich operators revisitedApr 25 2019The main object of this paper is to improve some of the known estimates for classical Kantorovich operators. A quantitative Voronovskaya-type result in terms of second moduli of continuity which improves some previous results is obtained. In order to ... More

Polynomial Roth theorems on sets of fractional dimensionsApr 25 2019Let $E\subset \mathbb{R}$ be a closed set of Hausdorff dimension $\alpha\in (0, 1)$. Let $P: \mathbb{R}\to \mathbb{R}$ be a polynomial without a constant term whose degree is bigger than one. We prove that if $E$ supports a probability measure satisfying ... More

On the Koebe Quarter Theorem for PolynomialsApr 24 2019D. Dimitrov has posed the problem of finding polynomials that set the sharpness of the Koebe Quarter Theorem for polynomials and asked whether Suffridge polynomials are optimal. We disprove Dimitrov's conjecture for polynomials of degree 3, 4, 5 and 6. ... More

Sufficient condition for rectifiability involving Wasserstein distance $W_2$Apr 24 2019A Radon measure $\mu$ is $n$-rectifiable if it is absolutely continuous with respect to $\mathcal{H}^n$ and $\mu$-almost all of $\text{supp}\,\mu$ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper we give two sufficient conditions for ... More

Necessary condition for rectifiability involving Wasserstein distance $W_2$Apr 24 2019A Radon measure $\mu$ is $n$-rectifiable if $\mu\ll\mathcal{H}^n$ and $\mu$-almost all of $\text{supp}\,\mu$ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper we give a necessary condition for rectifiability in terms of the so-called ... More

Low-dimensional maximal restriction principles for the Fourier transformApr 24 2019Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of convolution-type and $r-$average maximal functions. As a by-product of our ... More

Descartes' rule of signs and moduli of rootsApr 24 2019A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ ... More

A Non-Linear Roth Theorem for Fractals of Sufficiently Large DimensionApr 23 2019Suppose that $d \geq 2$, and that $A \subset [0,1]$ has sufficiently large dimension, $1 - \epsilon_d < \dim_H(A) < 1$. Then for any polynomial $P$ of degree $d$ with no constant term, there exists a point configuration $\{ x, x-t,x-P(t) \} \subset A$ ... More

Extra invariance of principal shift invariant spaces and the Zak transformApr 23 2019We prove a necessary and sufficient condition for a principal shift invariant space of $L^2(\mathbb{R})$ to be invariant under translations by the subgroup $\frac{1}{N} \mathbb{Z}, N>1$. This condition is given in terms of the Zak transform of the group ... More

Pointwise strong (H, Phi) approximation by Fourier series of L^{Psi} integrable functionsApr 23 2019We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H; Phi) as an approximation version of the Totik type generalization ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019Apr 25 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019May 01 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are ... More

Polarization, sign sequences and isotropic vector systemsApr 23 2019We determine the order of magnitude of the $n$th $\ell_p$-polarization constant of the unit sphere $S^{d-1}$ for every $n,d \geq 1$ and $p>0$. For $p=2$, we prove that extremizers are isotropic vector sets, whereas for $p=1$, we show that the polarization ... More

Bounds on strong unicity for Chebyshev approximation with bounded coefficientsApr 23 2019We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and Taylor. We make ... More

Two double-angle formulas of generalized trigonometric functionsApr 22 2019With respect to generalized trigonometric functions, since the discovery of double-angle formula for a special case by Edmunds, Gurka and Lang in 2012, no double-angle formulas have been found. In this paper, we will establish new double-angle formulas ... More

Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentialsApr 21 2019We obtain quasimode, eigenfunction and spectral projection bounds for Schr\"odinger operators, $H_V=-\Delta_g+V(x)$, on compact Riemannian manifolds $(M,g)$ of dimension $n\ge2$, which extend the results of the third author~\cite{sogge88} corresponding ... More

A continuous analogue of Erdős' $k$-Sperner theoremApr 21 2019A \emph{chain} in the unit $n$-cube is a set $C\subset [0,1]^n$ such that for every $\mathbf{x}=(x_1,\ldots,x_n)$ and $\mathbf{y}=(y_1,\ldots,y_n)$ in $C$ we either have $x_i\le y_i$ for all $i\in [n]$, or $x_i\ge y_i$ for all $i\in [n]$. We show that ... More

On the compactness of oscillation and variation of commutatorsApr 21 2019In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via the compactness ... More

Several characterizations of an n-inner product spaceApr 21 2019In this article we present some identities in an n-inner product space related to the standard n-inner product and we prove new results related to several inequalities in a n-inner product space and in an n-normed space. Among these inequalities we will ... More