arXiv subjects

Esra Güldoğan Lekesiz

Publications and source records attributed to Esra Güldoğan Lekesiz.

6 recordsLinked to original sources

arXiv2025

Finite bivariate biorthogonal I -- Konhauser polynomials

In this paper, a finite set of biorthogonal polynomials in two variables is produced using Konhauser polynomials. Some properties containing operational and integral representation, Laplace transform, fractional calculus operators of this family are studied. Also, computing Fourier transform for the new set, a new family of biorthogonal functions are derived via Parseval's identity. On the other hand, this finite set is modified by adding two new parameters in order to have semigroup property and construct fractional calculus operators. Further, integral equation and integral operator are also derived for the modified version.

math.CA↗

arXiv2025

Finite biorthogonal M matrix polynomials

This paper provides a finite pair of biorthogonal matrix polynomials and their finite biorthogonality, several recurrence relations, matrix differential equation, generating function and integral representation.

math.CA↗

arXiv2025

Finite bivariate biorthogonal $N$-Konhauser polynomials

A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $N_{n}^{(p)}(w)$ and the Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal $N$-Konhauser polynomials.

math.CA↗

arXiv2024

Finite Bivariate Biorthogonal M-Konhauser Polynomials

In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$, by choosing appropriate parameters in order to obtain a relation between the Jacobi Konhauser polynomials and this new finite bivariate biorthogonal polynomials $_{K}M_{n;\upsilon}^{(p,q)}(z,t)$ similar to the relation between the classical Jacobi polynomials $P_{n}^{(p,q)}(t)$ and the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$. Several properties like generating function, operational/integral representation are derived and some applications like fractional calculus, Fourier transform and Laplace transform are studied thanks to that new transition relation and the definition of finite bivariate M-Konhauser polynomials.

math.CA↗

arXiv2024

Finite biorthogonal polynomials suggested by the finite orthogonal polynomials $M_{n}^{(p,q)}(x)$

In this paper, we derive a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials $M_{n}^{(p,q)}(x)$. The corresponding biorthogonality relation is given. Some useful relations and properties, concluding differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for polynomials $M_{n}(p,q,\upsilon;x)$.

math.CA↗

arXiv2022

Fourier transform of the orthogonal polynomials on the unit ball

Fourier transform of multivariate orthogonal polynomials on the unit ball are obtained. By using Parseval's identity, a new family of multivariate orthogonal functions are introduced. The results are expressed in terms of the continuous Hahn polynomials.

math.CA↗