Hiroshima Mathematical Journal

A Paley-Wiener theorem for the inverse Fourier transform on some homogeneous spaces

S. Thangavelu

Full-text: Open access

Abstract

We formulate and prove a version of Paley-Wiener theorem for the inverse Fourier transforms on noncompact Riemannian symmetric spaces and Heisenberg groups. The main ingredient in the proof is the Gutzmer’s formula.

Article information

Source
Hiroshima Math. J., Volume 37, Number 2 (2007), 145-159.

Dates
First available in Project Euclid: 24 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1187916316

Digital Object Identifier
doi:10.32917/hmj/1187916316

Mathematical Reviews number (MathSciNet)
MR2345365

Zentralblatt MATH identifier
1143.22008

Subjects
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 43A90: Spherical functions [See also 22E45, 22E46, 33C55]

Keywords
Symmetric spaces Fourier transform Heisenberg group Gutzmer’s formula Paley-Wiener theorems

Citation

Thangavelu, S. A Paley-Wiener theorem for the inverse Fourier transform on some homogeneous spaces. Hiroshima Math. J. 37 (2007), no. 2, 145--159. doi:10.32917/hmj/1187916316. https://projecteuclid.org/euclid.hmj/1187916316


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