Results 41 to 50 of about 3,034 (119)

A Bochner Theorem for Dunkl Polynomials [PDF]

, 2011
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions.
Vinet, Luc, Zhedanov, Alexei
core   +5 more sources

Hermite and Gegenbauer polynomials in superspace using Clifford analysis

, 2007
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way.
Bartocci C, Berezin F A, Brackx F, Brackx F, Cnops J, De Bie H, De Bie H, De Bie H, De Bie H Sommen F, De Bie H Sommen F, Delanghe R, F Sommen, Gilbert J E, H De Bie, Leites D A, Leites D A   +15 more
core   +2 more sources

Generalized Gegenbauer orthogonal polynomials

Journal of Computational and Applied Mathematics, 2001
The aim of the author is to give a characterization of the so-called generalized Gegenbauer polynomials. He first shows the link between this functions and the classical Jacobi polynomials. Then he establishes both a differential-difference and a second order differential equation satisfied by these generalized polynomials.
openaire   +2 more sources

Some Properties of Generalized Gegenbauer Matrix Polynomials [PDF]

International Journal of Analysis, 2014
Various new generalized forms of the Gegenbauer matrix polynomials are introduced using the integral representation method, which allows us to express them in terms of Hermite matrix polynomials. Certain properties for these new generalized Gegenbauer matrix polynomials such as recurrence relations and expansion in terms of Hermite matrix polynomials ...
openaire   +1 more source

The cylindrical Fourier transform [PDF]

, 2010
In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that
A. Erdélyi, F. Brackx, F. Brackx, F. Brackx, F. Brackx, I.S. Gradshteyn   +5 more
core   +2 more sources

Fractional Q$Q$‐curvature on the sphere and optimal partitions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara, Juan Carlos Fernández, Alberto Saldaña   +2 more
wiley   +1 more source

Fundamental Solutions and Green's Functions for Certain Elliptic Differential Operators From a Pseudodifferential Algebra

Mathematical Methods in the Applied Sciences, Volume 48, Issue 13, Page 12654-12674, September 2025.
ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad, Gohar Flad‐Harutyunyan   +1 more
wiley   +1 more source

Semi‐analytical solution of axisymmetric indentation of poroelastic multi‐layer coating on a substrate

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 9, September 2025.
Abstract We propose a novel semi‐analytical solution of the indentation problem for a poroelastic multi‐layer system. This study addresses the time‐dependent behavior of materials, such as biological tissues, where mechanical properties vary within the structures.
Kotaro Miura, Makoto Sakamoto, Kazuhiko Sasagawa   +2 more
wiley   +1 more source

Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals [PDF]

Journal of Classical Analysis, 2013
In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials.
Cohl, Howard S., MacKenzie, Connor
openaire   +3 more sources

Time‐Series Factor Modeling and Selection

Journal of Financial Research, Volume 48, Issue 2, Page 839-875, Summer 2025.
Abstract The article proposes a statistical time‐series factor model that incorporates deterministic orthogonal trend polynomials. Such polynomials allow capturing variation in returns without initially identifying a set of robust time‐series factors.
Michael Michaelides
wiley   +1 more source