Complex Hermite polynomials: Their combinatorics and integral operators

DOI10.1090/S0002-9939-2014-12362-8zbMath1308.05009OpenAlexW2074408098MaRDI QIDQ5179309

Plamen C. Simeonov, Mourad E. H. Ismail

Publication date: 19 March 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2014-12362-8

zbMATH Keywords

eigenvaluescompletenesseigenfunctionsorthogonalityintegral operatorscomplex Hermite polynomialscombinatorics of linearization of productsmatchings of multisets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Integral operators (45P05) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (16)

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Cites Work

• New orthogonality relations for the Hermite polynomials and related Hilbert spaces
• Hermite polynomials and a duality relation for matchings polynomials
• Asymptotics of generalized derangements
• A class of generalized complex Hermite polynomials
• Analytic properties of complex Hermite polynomials
• Operational formulae for the complex Hermite polynomialsH_p,q(z, z¯)
• Holomorphic Hermite polynomials and a non-commutative plane
• Coherent states and Hermite polynomials on quaternionic Hilbert spaces
• Modular structures on trace class operators and applications to Landau levels
• Complex and real Hermite polynomials and related quantizations
• Combinatorial Applications of Hermite Polynomials
• Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials
• A combinatorial formula for the linearization coefficients of general Sheffer polynomials
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