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The orthogonal complement of the Hilbert space associated to holomorphic Hermite polynomials (1906.00187v1)
Published 1 Jun 2019 in math.CA and math.CV
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.