Gelfand transforms of polyradial Schwartz functions on the Heisenberg group

DOI10.1016/J.JFA.2007.06.010zbMath1128.43009OpenAlexW2014345374MaRDI QIDQ2461229

Fulvio Ricci, Bianca Di Blasio, Francesca Astengo

Publication date: 27 November 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2007.06.010

zbMATH Keywords

Heisenberg groupGelfand pairsgroup Fourier transformGelfand spectrumGelfand transformsapproximation by smooth rapidly decreasing functionspolyradial Schwartz functionsSchwartz extension

Mathematics Subject Classification ID

Analysis on specific locally compact and other abelian groups (43A70) Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis (43-06)

Related Items (16)

Gelfand transforms of \(\mathrm{SO}(3)\)-invariant Schwartz functions on the free group \(N_{3,2}\) ⋮ Geometric models for the spectra of certain Gelfand pairs associated with Heisenberg groups ⋮ Spectral multipliers on 2-step stratified groups. II ⋮ Nonlocal heat equations in the Heisenberg group ⋮ Paley-Wiener theorems for the \(\mathrm U(n)\)-spherical transform on the Heisenberg group ⋮ Schwartz correspondence for the complex motion group on \(\mathbb{C}^2\) ⋮ Spectral multipliers on 2-step stratified groups. I. ⋮ A Scalar-Valued Fourier Transform for the Heisenberg Group ⋮ Nilpotent Gelfand pairs and spherical transforms of Schwartz functions. I: Rank-one actions on the centre ⋮ Nilpotent Gelfand pairs and Schwartz extensions of spherical transforms via quotient pairs ⋮ On the Schwartz correspondence for Gelfand pairs of polynomial growth ⋮ Gelfand pairs on the Heisenberg group and Schwartz functions ⋮ Some spherical analysis related to the pairs \((U(n),H_n)\) and \((U(p,q),H_n),p + q = n\) ⋮ Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth ⋮ A generalized Gelfand pair attached to a 3-step nilpotent Lie group ⋮ Generalized Gelfand pairs associated to \(m\)-step nilpotent Lie groups

Cites Work

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• Deux cours d'analyse harmonique. École d'Été d'Analyse Harmonique de Tunis, 1984
• Fourier analysis on the Heisenberg group. I. Schwartz space
• A Tauberian theorem and tangential convergence for bounded harmonic functions on balls in \(\mathbb{C}^n\)
• Harmonic analysis on solvable extensions of H-type groups
• The spherical transform of a Schwartz function on the Heisenberg group
• Spectra for Gelfand pairs associated with the Heisenberg group
• A functional calculus for Rockland operators on nilpotent Lie groups
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms

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