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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 2017: 1.29

SCImago Journal Rank (SJR) 2017: 0.177
Source Normalized Impact per Paper (SNIP) 2017: 0.409

Mathematical Citation Quotient (MCQ) 2017: 0.21

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Harmonic analysis and generalized functional equations for the cosine

Driss Zeglami
  • Corresponding author
  • Department of Mathematics, ENSAM, Moulay Ismaïl University, BP 15290, Al Mansour, Meknès, Morocco
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/ Brahim Fadli / Samir Kabbaj
Published Online: 2015-08-12 | DOI: https://doi.org/10.1515/apam-2015-0040


Let G be a locally compact group and let μ be a regular, compactly supported, complex-valued Borel measure on G. In the present paper, we determine the continuous solutions f,g : G → ℂ of the functional equation ∫G {f(xyt) + f(xy -1t)}dμ(t) = 2g(x)f(y), x,yG, in terms of characters, additive maps and matrix elements of irreducible, two-dimensional representations of G. Many consequences of this result are presented.

Keywords: Kannappan's functional equation; character; additive map; irreducible representation

MSC: 39B32; 39B52

About the article

Received: 2015-06-11

Revised: 2015-07-05

Accepted: 2015-07-09

Published Online: 2015-08-12

Published in Print: 2016-01-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 7, Issue 1, Pages 41–49, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2015-0040.

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