Images of function and distribution spaces under the Bargmann transform

DOI10.1007/s11868-016-0165-9zbMath1388.46030arXiv1409.5238OpenAlexW2102491560MaRDI QIDQ2014205

Joachim Toft

Publication date: 10 August 2017

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5238

zbMATH Keywords

Bargmann transformGelfand-Shilov estimatesPilipović spaces

Mathematics Subject Classification ID

Topological linear spaces of test functions, distributions and ultradistributions (46F05) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (43)

Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians ⋮ An Excursion to Multiplications and Convolutions on Modulation Spaces ⋮ Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipović kernels ⋮ Continuity properties for Born-Jordan operators with symbols in Hörmander classes and modulation spaces ⋮ Wick and anti-Wick characterizations of linear operators on spaces of power series expansions ⋮ Wave-front sets in non-quasianalytic setting for Fourier Lebesgue and modulation spaces ⋮ Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces ⋮ Paley-Wiener properties for spaces of entire functions ⋮ Periodic distributions and periodic elements in modulation spaces ⋮ Characterizations of a class of Pilipović spaces by powers of harmonic oscillator ⋮ Strong ultra-regularity properties for positive elements in the twisted convolutions ⋮ Hypercyclic exponential of the differential operator on Banach spaces related to Fock spaces ⋮ Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces ⋮ Continuity of Gevrey-Hörmander pseudo-differential operators on modulation spaces ⋮ Pseudo-differential operators on Orlicz modulation spaces ⋮ Pseudo-differential calculus in anisotropic Gelfand-Shilov setting ⋮ Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators ⋮ Pseudo-differential calculus in a Bargmann setting ⋮ A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform ⋮ Pseudo-differential Calculi and entropy estimates with Orlicz modulation spaces ⋮ A special orthogonal complement basis for holomorphic-Hermite functions and associated 1d- and 2d-fractional Fourier transforms ⋮ Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces ⋮ The Gabor wave front set in spaces of ultradifferentiable functions ⋮ Paley–Wiener properties for spaces of power series expansions ⋮ Pseudo-differential operators in a Gelfand-Shilov setting ⋮ The Zak transform on Gelfand-Shilov and modulation spaces with applications to operator theory ⋮ Anisotropic Gevrey-Hörmander Pseudo-Differential Operators on Modulation Spaces ⋮ Extended Gevrey Regularity via the Short-Time Fourier Transform ⋮ Wiener Estimates on Modulation Spaces ⋮ FRACTIONAL INTEGRAL OPERATORS ON -MODULATION SPACES IN THE FULL RANGE ⋮ The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces ⋮ Schatten properties, nuclearity and minimality of phase shift invariant spaces ⋮ Compactness properties for modulation spaces ⋮ Spaces of type \(S\) as topological algebras under twisted convolution and star product ⋮ A characterization of modulation spaces by symplectic rotations ⋮ Subexponential decay and regularity estimates for eigenfunctions of localization operators ⋮ Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces ⋮ Tensor products for Gelfand-Shilov and Pilipović distribution spaces ⋮ The Weyl product on quasi-Banach modulation spaces ⋮ Anisotropic Shubin operators and eigenfunction expansions in Gelfand-Shilov spaces ⋮ Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity ⋮ Fourier characterizations of Pilipović spaces ⋮ Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type

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