A Scalar-Valued Fourier Transform for the Heisenberg Group

DOI10.1007/978-3-031-37800-3_7arXiv2206.00883OpenAlexW4387916188MaRDI QIDQ6194486

Sundaram Thangavelu

Publication date: 19 March 2024

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.00883

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Analysis on other specific Lie groups (43A80) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

• L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group
• Paley-Wiener theorems for the \(\mathrm U(n)\)-spherical transform on the Heisenberg group
• Harmonic analysis as spectral theory of Laplacians
• Gelfand pairs on the Heisenberg group and Schwartz functions
• Fourier analysis on the Heisenberg group. I. Schwartz space
• The spherical transform of a Schwartz function on the Heisenberg group
• Harmonic analysis on the Heisenberg group
• An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
• On Paley-Wiener theorems for the Heisenberg group
• A frequency space for the Heisenberg group
• Gelfand transforms of polyradial Schwartz functions on the Heisenberg group
• Interpolation of Operators with Change of Measures
• Harmonic Analysis in Phase Space. (AM-122)
• Fourier transform of Schwartz functions on the Heisenberg group
• An analogue of Ingham's theorem on the Heisenberg group
• Analogues of theorems of Chernoff and Ingham on the Heisenberg group
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