Title

COMPLEX HERMITE POLYNOMIALS: THEIR COMBINATORICS AND INTEGRAL OPERATORS

Authors

Authors

M. E. H. Ismail;P. Simeonov

Comments

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Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

Complex Hermite polynomials; matchings of multisets; orthogonality; combinatorics of linearization of products; eigenvalues; eigenfunctions; integral operators; completeness; LINEARIZATION COEFFICIENTS; SHEFFER POLYNOMIALS; SPACES; Mathematics, Applied; Mathematics

Abstract

We consider two types of Hermite polynomials of a complex variable. For each type we obtain combinatorial interpretations for the linearization coefficients of products of these polynomials. We use the combinatorial interpretations to give new proofs of several orthogonality relations satisfied by these polynomials with respect to positive exponential weights in the complex plane. We also construct four integral operators of which the first type of complex Hermite polynomials are eigenfunctions and we identify the corresponding eigenvalues. We prove that the products of these complex Hermite polynomials are complete in certain L-2-spaces.

Journal Title

Proceedings of the American Mathematical Society

Volume

143

Issue/Number

4

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

1397

Last Page

1410

WOS Identifier

WOS:000351745400004

ISSN

0002-9939

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