Three systems of orthogonal polynomials and L2-boundedness of two associated operators

In this paper, we describe three systems of orthogonal polynomials belonging to the class of Meixner–Pollaczek polynomials, and establish some useful connections between them in terms of three basic operators that are related to them. Furthermore, we investigate boundedness properties of two other o...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-03, Vol.459 (1), p.464-475
Main Authors: Musonda, John, Kaijser, Sten
Format: Article
Language:English
Subjects:
Convolution operator
Hilbert space
Orthonormal basis
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Summary:In this paper, we describe three systems of orthogonal polynomials belonging to the class of Meixner–Pollaczek polynomials, and establish some useful connections between them in terms of three basic operators that are related to them. Furthermore, we investigate boundedness properties of two other operators, both as convolution operators in the translation invariant case where we use Fourier transforms and for the weights related to the relevant orthogonal polynomials. We consider only the most important but also simplest case of L2-spaces. However, in subsequent papers, we intend to extend the study to Lp-spaces (1
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.10.040