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A Paley–Wiener theorem for some eigenfunction expansions
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S. Thangavelu
Published/Copyright:
November 15, 2010
Abstract
We prove a general version of Paley–Wiener theorem characterising functions with finite Fourier expansions. The result covers Fourier series on compact symmetric spaces, Hermite and special Hermite expansions as particular cases. Gutzmer's formula plays an important role in the formulation and proof of the theorem.
Keywords.: Segal–Bargmann transform; Hermite and Laguerre functions; Heisenberg groups; Symmetric spaces
Received: 2010-03-03
Accepted: 2010-09-29
Published Online: 2010-11-15
Published in Print: 2011-September
© de Gruyter 2011
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Keywords for this article
Segal–Bargmann transform;
Hermite and Laguerre functions;
Heisenberg groups;
Symmetric spaces
Articles in the same Issue
- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
