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Three systems of orthogonal polynomials and L2-boundedness of associated operators
(Mathematics/Applied Mathematics)ORCID iD: 0000-0001-7682-870X
Uppsala University, Sweden.
2018 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 459, no 1, p. 464-475Article in journal (Other academic) Published
Abstract [en]

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 L-2-spaces. However, in subsequent papers, we intend to extend the study to L-p-spaces (1 < p < infinity). 

Place, publisher, year, edition, pages
2018. Vol. 459, no 1, p. 464-475
Keywords [en]
orthonormal basis, Hilbert space, convolution operator.
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-29566DOI: 10.1016/j.jmaa.2017.10.040ISI: 000418310900027OAI: oai:DiVA.org:mdh-29566DiVA, id: diva2:872281
Available from: 2015-11-18 Created: 2015-11-18 Last updated: 2018-01-05Bibliographically approved

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Musonda, John

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