Related papers: Higher-order interlacing for matrix-valued meromor…

Using as starting point a classical integral representation of a L-function we define a familly of two variables extended functions which are eigenfunctions of a Hermitian operator (having imaginary part of zeros as eigenvalues). This…

In this paper, for every $q\in(0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $\alpha, 0\le\alpha<1$. In addition, we discuss the Fekete-szeg\"o…

We consider the Dirichlet series associated to the number of representations of an integer as the sum of primes. Assuming the Riemann hypothesis on the distribution of the zeros of the Riemann zeta function we obtain the domain of…

The classical representation problem for a meromorphic function f in C^n, n>=1, consists in representing f as the quotient f=g/h of two entire functions g and h, each with logarithm of modulus majorized by a function as close as possible to…

If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…

The concept of a fully interlacing matrix of formal power series with real coefficients is introduced. This concept extends and strengthens that of an interlacing sequence of real-rooted polynomials with nonnegative coefficients, in the…

Necessary and sufficient conditions for the interlacing of the zeros of cylinder functions and their derivatives of different orders are given.

We study statistical and algorithmic aspects of using hypergraphons, that are limits of large hypergraphs, for modeling higher-order interactions. Although hypergraphons are extremely powerful from a modeling perspective, we consider a…

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…

We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…

We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the…

Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Notebook actually lives in the realms of this theory. As a…

Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…

We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of those functional relations is given by the symmetry with…

We identify a class of remarkable algebraic relations satisfied by the zeros of the Krall orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two. Given an orthogonal polynomial family…

The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the Hilbert function of algbebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper…

We introduce Omega functions that generalize Euler Gamma functions and study the functional difference equation they satisfy. Under a natural exponential growth condition, the vector space of meromorphic solutions of the functional equation…

Range functions are a fundamental tool for certified computations in geometric modeling, computer graphics, and robotics, but traditional range functions have only quadratic convergence order ($m=2$). For ``superior'' convergence order…

We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker's distributions. The range of correlation of the B-spline copulas is examined, and the Frechet--Hoeffding upper bound is proved…

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…