Related papers: Schur analysis and discrete analytic functions: Ra…

In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions,…

A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of…

In this note, we use Rouch\'e's theorem and the pleasant properties of the arithmetic of the logarithmic derivative to establish several new results regarding the geometry of the zeros, poles, and critical points of a rational function.…

We prove a discrete approximation of functionals with jumps and creases.

We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular partitions. We prove the relations as an…

Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function…

We construct of a family of fundamental solutions for elliptic partial differential operators with real constant coefficients. The elements of such a family are expressed by means of jointly real analytic functions of the coefficients of…

Let $X\subset{\mathbb R}^n$ be a (global) real analytic surface. Then every positive semidefinite meromorphic function on $X$ is a sum of $10$ squares of meromorphic functions on $X$. As a consequence, we provide a real Nullstellensatz for…

This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on Schur convex function are established. In the wake of the…

Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form…

For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded…

Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…

We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for…

In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…

We introduce the notion of $R$-analytic functions. These are definable in an o-minimal expansion of a real closed field $R$ and are locally the restriction of a $K$-differentiable function (defined by Peterzil and Starchenko) where…

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that singular Schwartz distributions can be represented within that same…