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

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

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 rep...

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Veröffentlicht in:arXiv.org 2019-06
Hauptverfasser: Abdelhadi Benahmadi, Ghanmi, Allal, Mohammed Souid El Ainin
Format: Artikel
Sprache:eng
Schlagworte:
Hermite polynomials
Hilbert space
Integral transforms
Kernel functions
Mathematical analysis
Monte Carlo simulation
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Zusammenfassung: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.
ISSN:2331-8422