Hermite Polynomials in Dunkl-Clifford Analysis

2011/02/10 by Minggang Feiyz, Minggang Fei, Paula Cerejeiras +4
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics #math.CV

paper · pdf · doi:10.48550/arxiv.1102.2036

17 pages

arxiv created 2011/02/10 · openalex publication_date 2011/02/10 · arxiv updated 2011/02/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we present a generalization of the classical Hermite polynomials to the framework of Clifford-Dunkl operators. Several basic properties, such as orthogonality relations, recurrence formulae and associated differential equations, are established. Finally, an orthonormal basis for the Hilbert modules arising from the corresponding weight measures is studied.

Citations

• Differential-difference operators associated to reflection groups

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