Bounds on the Segal-Bargmann transform of \(L^p\) functions

DOI10.1007/BF02513076zbMath1003.44005arXivmath-ph/0103001MaRDI QIDQ1602280

Brian C. Hall

Publication date: 2 February 2003

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0103001

zbMATH Keywords

coherent statesinversion formulasSegal-Bargmann transformwindowed Fourier transformsholomorphic convolution transforms

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Function spaces arising in harmonic analysis (42B35) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items

A \(q\)-deformation of the true-polyanalytic Bargmann transform, Isometry theorem for the Segal-Bargmann transform on a noncompact symmetric space of the complex type, A quaternionic analogue of the Segal-Bargmann transform, Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform, The slice hyperholomorphic Bergman space on \(\mathbb {B}_{R}\): integral representation and asymptotic behavior, The Bargmann transform on \(L^p(\mathbb{R})\), Image of \(L^{p}(\mathbb R^{n})\) under the Hermite semigroup, Coherent state transforms attached to generalized Bargmann spaces on the complex plane, A \(q\)-deformation of true-polyanalytic Bargmann transforms when \(q^{-1}>1\), Injectivity of Gabor phase retrieval from lattice measurements

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