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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

CiteScore 2018: 0.43

SCImago Journal Rank (SJR) 2018: 0.140
Source Normalized Impact per Paper (SNIP) 2018: 0.576

Mathematical Citation Quotient (MCQ) 2017: 0.21

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A Paley–Wiener theorem for some eigenfunction expansions

S. Thangavelu
Published Online: 2010-11-15 | DOI: https://doi.org/10.1515/apam.2010.042


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

About the article

Received: 2010-03-03

Accepted: 2010-09-29

Published Online: 2010-11-15

Published in Print: 2011-09-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 2, Issue 3-4, Pages 451–466, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2010.042.

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