arXiv subjects

Rabia Aktaş Karaman

Publications and source records attributed to Rabia Aktaş Karaman.

4 recordsLinked to original sources

arXiv2026

Finite orthogonal polynomials on a cone

The aim of this paper is to study finite orthogonal polynomials on a cone of revolution and its surface. We define two classes of finite orthogonal polynomials on the solid cone and derive their corresponding differential equations and recurrence relations. Furthermore, we demonstrate that, in the limit case, one of these classes reduces to Laguerre polynomials on the cone. Similarly, we establish two families of finite orthogonal polynomials on the surface of the cone and analyze their respective properties.

math.CA↗

arXiv2025

Fourier transforms of orthogonal structures on the paraboloid

The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of multivariate orthogonal functions by using Parseval's identity. In addition, some contiguous relations for these families of functions are given, and the obtained results are expressed in terms of the continuous Hahn polynomials.

math.CA↗

arXiv2024

Chlodowsky variant of Bernstein-type operators on the domain

In the present paper, we deal with Bernstein-Chlodowsky type operators for approximating functions on the domain. We first present Bernstein-Chlodowsky type operators in two variables and then we discuss some examples of these operators under a domain transformation. Finally, we give bivarite shifted mth Bernstein-Chlodowsky-Stancu operators and we present some figures for approximation properties of our operator.

math.GM↗

arXiv2024

Fourier transforms of orthogonal polynomials on the cone

The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal polynomials on the cone such as Laguerre polynomials on the cone and Jacobi polynomials on the cone and to define two new families of multivariate orthogonal functions by using Parseval's identity. Also, the obtained results are expressed in terms of the continuous Hahn polynomials.

math.CA↗