Three systems of orthogonal polynomials and L2-boundedness of associated operators
(English)Manuscript (preprint) (Other academic)
We describe three systems of orthogonal polynomials belonging to the class of Meixner-Pollaczek polynomials, and establish some useful connections between in terms of operators that are related to them. It turns out that two of these operators are singular integrals and in this paper we investigate their boundedness properties, both as convolution operators in the translation invariant case where we use Fourier transforms and in the weighted case where we use the orthogonal polynomials. It is proved that in both cases these two operators are bounded on the L2-spaces, and estimates of the norms are obtained.
orthonormal basis, Hilbert space, convolution operator.
Research subject Mathematics/Applied Mathematics
IdentifiersURN: urn:nbn:se:mdh:diva-29566OAI: oai:DiVA.org:mdh-29566DiVA: diva2:872281
This preprint manuscript has been submitted for publication somewhere.2015-11-182015-11-182015-11-19Bibliographically approved