The orthogonal complement of the Hilbert space associated to holomorphic Hermite polynomials

2019/06/01 by Abdelhadi Benahmadi, Benahmadi, Abdelhadi, Allal Ghanmi +3
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1906.00187

openalex publication_date 2019/06/01 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28

Abstract

We study the orthogonal complement of the Hilbert subspace considered by by van Eijndhoven and Meyers in [J. Math. Anal. Appl. 146 (1990), no. 1, 89--98 and associated to holomorphic Hermite polynomials. A polyanalytic orthonormal basis is given and the explicit expressions of the corresponding reproducing kernel functions and Segal--Bargmann integral transforms are provided.

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