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Three systems of orthogonal polynomials and L-2-boundedness of two associated operators
Malardalen Univ, Div Appl Math, Box 883, S-72123 Vasteras, Sweden..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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 (Refereed) 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
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2018. Vol. 459, no 1, p. 464-475
Keywords [en]
Orthonormal basis, Hilbert space, Convolution operator
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-338945DOI: 10.1016/j.jmaa.2017.10.040ISI: 000418310900027OAI: oai:DiVA.org:uu-338945DiVA, id: diva2:1175738
Available from: 2018-01-18 Created: 2018-01-18 Last updated: 2018-01-18Bibliographically approved

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Kaijser, Sten

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