Construction of Weighted Clifford Prolate Spheroidal wave Functions
Hamed Baghal Ghaffari, Swanhild Bernstein
TL;DR
This paper introduces weighted Clifford prolate spheroidal wave functions, exploring their properties, orthogonality, and related Clifford Gegenbauer polynomials, advancing the mathematical framework for these functions.
Contribution
It defines and constructs weighted Clifford prolate spheroidal wave functions and proves their orthogonality in a weighted space, extending existing mathematical theory.
Findings
Properties of Clifford Gegenbauer polynomials derived
Orthogonality of the new functions established
Bonnet formula for Clifford Gegenbauer polynomials proved
Abstract
We develop some properties and the Bonnet formula for Clifford Gegenbauer polynomials. Then after we define and construct weighted Clifford prolate spheroidal wave functions. We then prove that they are orthogonal in a weighted function space.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Mathematical functions and polynomials