Mean periodic functions on phase space and the Pompeiu problem with a twist

DOI10.5802/aif.1482zbMath0831.43003OpenAlexW2001439337MaRDI QIDQ1903303

Sundaram Thangavelu

Publication date: 28 November 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1995__45_4_1007_0

zbMATH Keywords

spherical functionsrepresentationsmean periodic functionsPompeiu problemWeyl transformPaley- Wiener theoremreduced Heisenberg groupFourier-Weyl transform

Mathematics Subject Classification ID

Classical almost periodic functions, mean periodic functions (42A75) Analysis on specific locally compact and other abelian groups (43A70)

Related Items (7)

An analog of the Schwartz theorem on spectral analysis on a hyperbolic plane ⋮ An analog of the Brown-Schreiber-Taylor theorem for weighted hyperbolic shifts ⋮ Reconstruction of continuous functions from locally uniform weighted averages ⋮ Spectral synthesis on the reduced Heisenberg group ⋮ Analogues of the Liouville theorem for solutions of the twisted convolution equation ⋮ Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group ⋮ Poisson transform for the Heisenberg group and eigenfunctions of the sublaplacian

Cites Work

• Unnamed Item
• The Pompeiu problem revisited
• Spherical mean periodic functions on semi simple Lie groups
• Counterexamples to a problem of L. Schwartz
• On Schwartz's theorem for the motion group
• A Paley-Wiener theorem for step two nilpotent Lie groups
• Injectivity of the Pompeiu transform in the Heisenberg group
• Spherical means and CR functions on the Heisenberg group
• On regularity of twisted spherical means and special Hermite expansions
• On Paley-Wiener theorems for the Heisenberg group
• Spectral synthesis and the Pompeiu problem
• Théorie générale des fonctions moyenne-périodiques
• Harmonic Analysis in Phase Space. (AM-122)

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