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Quotient Problem For Entire Functions with Moving TargetsFeb 21 2019As an analogue of the Hadamard quotient problem in number theory, the quotient problem (in the sense of complex entire functions) for two sequences $F(n)=a_0+a_1f_1^n+\cdots+a_lf_l^n$ and $ G(n)=b_0+b_1g_1^n+\cdots+b_mg_m^n$, has been solved, where the ... More Quasi-trees and geodesic treesFeb 20 2019A quasi-tree is a metric tree that is doubling and of bounded turning. We prove that every quasi-tree can be mapped to a geodesic tree by a quasisymmetric homeomorphism. We also show that every quasi-tree has conformal dimension equal to $1$. Row contractions annihilated by interpolating vanishing idealsFeb 18 2019We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how ... More A four dimensional Jensen formulaFeb 18 2019We prove a Jensen formula for slice-regular functions of one quaternionic variable. The formula relates the value of the function and of its first two derivatives at a point with its integral mean on a three dimensional sphere centred at that point and ... More The isometries of the space of Kähler metricsFeb 16 2019Given a compact K\"ahler manifold, we prove that all global isometries of the space of K\"ahler metrics are induced by biholomorphisms and anti-biholomorphisms of the manifold. In particular, there exist no global symmetries for Mabuchi's metric. Moreover, ... More Outer functions and divergence in de Branges-Rovnyak spacesFeb 15 2019In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function $f$ can be approximated in norm by its dilates $f_r(z):=f(rz)~(r<1)$, in other words, $\lim_{r\to1^-}\|f_r-f\|=0$. We construct a de Branges-Rovnyak ... More Linear maps preserving inner functionsFeb 15 2019We show that, for many holomorphic function spaces on the unit disk, a continuous endomorphism that sends inner functions to inner functions is necessarily a weighted composition operator. Monge-Ampère of Pac-ManFeb 13 2019We show that the Monge-Amp\`ere density of the extremal function $V_P$ for a non-convex Pac-Man set $P\subset {\bf R}^2$ tends to a finite limit as we approach the vertex $p$ of $P$ linearly but with a value that may vary with the line. On the other hand, ... More On factorization of p-adic meromorphic functionsFeb 13 2019In this paper, we study primeness and pseudo primeness of p-adic meromorphic functions. We also consider left (resp. right ) primeness of these functions. We give, in particular, sufficient conditions for a meromorphic function to satisfy such properties. ... More Elliptic extension of Gustafson's $q$-integral of type $G_2$Feb 13 2019The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a special limiting ... More Identifying logarithmic tractsFeb 12 2019We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct ... More Carleson measures on simply connected domainsFeb 12 2019We study the Carleson measures associated to the Hardy and weighted Bergman spaces defined on general simply connected domains. This program was initiated by Zinsmeister in his paper \textit{Les domaines de Carleson }(1989), where he shows that the geometry ... More Doubly periodic monopoles and $q$-difference modulesFeb 10 2019An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue ... More $(g,k)$-Fermat curvesFeb 08 2019Let $G$ be a co-compact torsion free Fuchsian group of genus $g \geq2$ and, for each integer $k \geq 2$, $G_{k}$ be its normal subgroup generated by the $k$-powers of the elements of $G$ together its commutators. There is a natural holomorphic embedding ... More An analytic approach to the Riemann hypothesisFeb 07 2019In this work we consider a new functional equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent ... More Separation of variables in the semistable rangeFeb 07 2019In this paper, we give an alternative proof of separation of variables for scalar-valued polynomials $P:(\mathbb R^m)^k\to\mathbb C$ in the semistable range $m\geq 2k-1$ for the symmetry given by the orthogonal group $O(m)$. It turns out that uniqueness ... More Starlikeness Associated With The Exponential FunctionFeb 07 2019Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential ... More On a problem of PichoridesFeb 06 2019Let $S^{(\Lambda)}$ denote the classical Littlewood-Paley square function formed with respect to a lacunary sequence $\Lambda$ of positive integers. Motivated by a remark of Pichorides, we obtain sharp asymptotic estimates of the behaviour of the operator ... More LCK metrics on toric LCS manifoldsFeb 06 2019We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs $(C,a)$, where $C$ is a good cone in the dual Lie algebra of the torus and $a$ is a positive real number. ... More Schur parameters and Carathéodory classFeb 06 2019The Schur (resp. Carath\'eodory) class consists of all the analytic functions $f$ on the unit disk with $|f|\le 1$ (resp. $\Re f>0$ and $f(0)=1$). The Schur parameters $\gamma_0,\gamma_1,\dots (|\gamma_j|\le 1)$ are known to parametrize the coefficients ... More Geometric pluripotential theory on Kähler manifoldsFeb 06 2019Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively ... More Notes on the Szego minimum problem. II. Singular measuresFeb 03 2019In this part, we prove several quantitative results concerning with the Szego minimum problem for classes of measure on the unit circle concentrated on small subsets. As a by-product, we refute one conjecture of Nevai. This note can be read independently ... More Hodge cycles for cubic hypersurfacesFeb 03 2019We study an algebraic cycle of the form $Z_0= r {\mathbb P}^{\frac{n}{2}}+\check r \check{\mathbb P}^{\frac{n}{2}}$, $r \in{\mathbb N},\check r \in{\mathbb Z},\ \ 1\leq r , |\check r |\leq 10,\ \ \gcd ( r ,\check r )=1$, inside the cubic Fermat variety ... More A Conjecture of TrautmanFeb 01 2019In 1998 the physicist Andre Trautman conjectured that a three-dimensional CR manifold is locally realizable if and only if its canonical bundle admits a closed nowhere zero section. We review the relevant definitions, give the physical context, and outline ... More Algebraic surfaces with infinitely many twistor linesJan 31 2019Feb 04 2019We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give ... More Meromorphic limits of automorphismsJan 30 2019Let $X$ be a compact complex manifold in the Fujiki class $\mathscr{C}$. We study the compactification of $\operatorname{Aut}^0(X)$ given by its closure in Barlet cycle space. The boundary points give rise to non-dominant meromorphic self-maps of $X$. ... More Deformation limit of Moishezon manifoldsJan 30 2019Let $\pi: \mathcal{X}\rightarrow \Delta$ be a holomorphic family of compact complex manifolds over an open disk in $\mathbb{C}$. If the fiber $X_t:=\pi^{-1}(t)$ for each nonzero $t$ in an uncountable subset $B$ of $\Delta$ is Moishezon and the reference ... More CURE: Curvature Regularization For Missing Data RecoveryJan 28 2019Missing data recovery is an important and yet challenging problem in imaging and data science. Successful models often adopt certain carefully chosen regularization. Recently, the low dimension manifold model (LDMM) was introduced by S.Osher et al. and ... More On a trace formula for functions of noncommuting operatorsJan 28 2019The main result of the paper is that the Lifshits--Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that for pairs $(A_1,B_1)$ and $(A_2,B_2)$ of bounded self-adjoint operators ... More Zeros of Normalized Sections of Non Convergent Power SeriesJan 25 2019A well known result due to Carlson affirms that a power series with finite and positive radius of convergence R has no Ostrowski gaps if and only if the sequence of zeros of its nth sections is asymptotically equidistributed to {|z|=R}. Here we extend ... More On a generalization of the Gaussian plane to three dimensionsJan 24 2019Each associative division algebra over the real number field of finite dimension $n \in \mathbb{N}$ is isomorphic (1) to $\mathbb{R}$ (the field of all real numbers, $n=1$), or, (2) to $\mathbb{C}$ (the field of all Gaussian complex numbers, $n=2$), or, ... More Sharp Complex Convexity EstimatesJan 23 2019In this paper we determine the value of the best constants in the 2-uniform PL-convexity estimates of $\mathbb C$. This solves a problem posed by W. J. Davis, D. J. H. Garling and N. Tomczak-Jaegermann. The equivalence principle for almost periodic functionsJan 22 2019Given two arbitrary almost periodic functions, we prove that the existence of a common open vertical strip $V$, where both functions assume the same set of values on every open vertical substrip included in $V$, is a necessary and sufficient condition ... More Extremal problems for polynomials with real rootsJan 22 2019We consider polynomials of degree $d$ with only real roots and a fixed value of discriminant, and study the problem of minimizing the absolute value of polynomials at a fixed point off the real line. There are two types of polynomials that turn out to ... More Maximum Principles for Matrix-Valued Analytic FunctionsJan 22 2019To what extent is the maximum modulus principle for scalar-valued analytic functions valid for matrix-valued analytic functions? In response, we discuss some maximum norm principles for such functions that do not appear to be widely known, deduce maximum ... More Besov spaces induced by doubling weightsJan 21 2019Let $1\le p<\infty$, $0<q<\infty$ and $\nu$ be a two-sided doubling weight satisfying $$\sup_{0\le r<1}\frac{(1-r)^q}{\int_r^1\nu(t)\,dt}\int_0^r\frac{\nu(s)}{(1-s)^q}\,ds<\infty.$$ The weighted Besov space $\mathcal{B}_{\nu}^{p,q}$ consists of those ... More On Hölder continuity of mappings in domains and on boundariesJan 18 2019We study mappings with branching of a domain of Euclidean space. The H\"older and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition, we found conditions ... More Isoperimetric inequalities for Bergman analytic contentJan 17 2019The Bergman $p$-analytic content ($1\leq p<\infty $) of a planar domain $\Omega $ measures the $L^{p}(\Omega )$-distance between $\overline{z}$ and the Bergman space $A^{p}(\Omega )$ of holomorphic functions. It has a natural analogue in all dimensions ... More Symmetries of Transversely Projective FoliationsJan 17 2019Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index subgroup of PsAut(X, ... More Quasisymmetric embeddings of slit Sierpiński carpetsJan 17 2019In this paper we study the problem of quasisymmetrically embedding metric carpets, i.e., spaces homeomorphic to the classical Sierpi\'nski carpet, into the plane. We provide a complete characterization in the case of so-called dyadic slit carpets. The ... More Spiders' webs in the punctured planeJan 16 2019Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane. We give several ... More A Newton method for harmonic mappings in the planeJan 16 2019We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit. For zeros ... More Algorithms for $\ell_p$-based semi-supervised learning on graphsJan 15 2019We develop fast algorithms for solving the variational and game-theoretic $p$-Laplace equations on weighted graphs for $p>2$. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in semi-supervised ... More Quadratization in discrete optimization and quantum mechanicsJan 14 2019A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used in QMA completeness ... Morequant-phcs.CVcs.DMmath.OCphysics.chem-ph05C50, 11A41, 11A51, 11N35, 11N36, 11N80, 11Y05, 65K10, 65P10,
65Y20, 68Q12, 81P68, 81P94, 94A60, 81-08B.2.4; B.8.2; C.1.3; C.1.m; F.2.1; F.2.3; F.4.1; G.1.0; G.1.3;
G.1.5; G.1.6; G.2.0; G.2.1; I.1.2; I.6.4; C.4; E.3; G.0; J.2; K.2 Remarks on Chern-Einstein Hermitian metricsJan 14 2019We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself. Adiabatic Limit and Deformations of Complex StructuresJan 13 2019Based on our recent adaptation of the adiabatic limit construction to the case of complex structures, we give a new proof of the fact, that we first proved in 2009 and 2010, that the deformation limiting manifold of any holomorphic family of Moishezon ... More Fréchet-valued formal power seriesJan 12 2019Let $A$ be a non-projectively-pluripolar set in a Fr\'{e}chet space $E.$ We give sufficient conditions to ensure the convergence on some zero-neighbourhood in $E$ of a (sequence of) formal power series of Fr\'{e}chet-valued continuous homogeneous polynomials ... More