Complex Hermite Polynomials: Their Combinatorics And Integral Operators

Keywords

Combinatorics of linearization of products; Completeness; Complex Hermite polynomials; Eigenfunctions; Eigenvalues; Integral operators; Matchings of multisets; Orthogonality

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 L2-spaces.

Publication Date

1-1-2015

Publication Title

Proceedings of the American Mathematical Society

Volume

143

Issue

4

Number of Pages

1397-1410

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-2014-12362-8

Socpus ID

84923239743 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84923239743

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