Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators

DOI10.1007/S00041-023-10009-3zbMath1519.46031arXiv2202.00938OpenAlexW4376602394MaRDI QIDQ6103435

Albin Petersson

Publication date: 5 June 2023

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

Full work available at URL: https://arxiv.org/abs/2202.00938

zbMATH Keywords

ultradistributionsToeplitz operatorsGelfand-Shilov spacesshort-time Fourier transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) (H^p)-spaces (42B30) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (3)

Microlocal analysis for Gelfand-Shilov spaces ⋮ Propagation of anisotropic Gabor singularities for Schrödinger type equations ⋮ Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

Cites Work

• Quantum coherent operators: A generalization of coherent states
• Foundations of time-frequency analysis
• Spaces of test functions via the STFT
• Images of function and distribution spaces under the Bargmann transform
• A projective description of generalized Gelfand-Shilov spaces of Roumieu type
• An algebra of pseudodifferential operators and quantum mechanics in phase space
• Characterizations of the Gelfand-Shilov spaces via Fourier transforms
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