A Paley–Wiener theorem for some eigenfunction expansions

A Paley–Wiener theorem for some eigenfunction expansions

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...

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Veröffentlicht in:Advances in pure and applied mathematics (Berlin, Germany) Germany), 2011-09, Vol.2 (3-4), p.451-466
1. Verfasser: Thangavelu, S.
Format: Artikel
Sprache:eng
Schlagworte:
Heisenberg groups
Hermite and Laguerre functions
Segal–Bargmann transform
Symmetric spaces
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Zusammenfassung: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.
ISSN:1867-1152
1869-6090
DOI:10.1515/apam.2010.042