A Theorem on Difference Polynomials

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

Elements of Pólya-schur Theory in Finite Difference Setting

The Pólya-Schur theory describes the class of hyperbolicity preservers, i.e., the linear operators on univariate polynomials preserving realrootedness. We attempt to develop an analog of Pólya-Schur theory in the setting of linear finite difference operators. We study the class of linear finite difference operators preserving the set of real-rooted polynomials whose mesh (i.e., the minimal dist...

Q-classical Orthogonal Polynomials: a General Difference Calculus Approach

It is well known that the classical families of orthogonal polynomials are characterized as the polynomial eigenfunctions of a second order homogenous linear differential/difference hypergeometric operator with polynomial coefficients. In this paper we present a study of the classical orthogonal polynomials sequences, in short classical OPS, in a more general framework by using the differential...