COMPLEX HERMITE POLYNOMIALS: THEIR COMBINATORICS AND INTEGRAL OPERATORS

    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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