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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Managing Editor: Bezzarga, Mounir / Kamoun, Lotfi / Karoui, Abderrazek / Mili, Maher

Editorial Board Member: Faraut, Jacques / Koornwinder, Tom H. / Lannes, Jean / Sifi, Mohamed / Temam, Roger / Zaag, Hatem / Zarati, Said / Aldroubi, Akram / Anker, Jean-Philippe / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Beznea, Lucian / Bonami, Aline / Cahen, Paul-Jean / Chemin, Jean-Yves / Demailly, Jean-Pierre / El Mir, Hassine / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jouini, Elyes / Maday, Yvon / Maeda, Yoshiaki / Mustapha, Sami / Ovsienko, Valentin / Pouzet, Maurice / Prestin, Jürgen / Radulescu, Vicentiu / Schwartz, Lionel / Kobayashi, Toshiyuki

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.342
Source Normalized Impact per Paper (SNIP) 2015: 0.554
Impact per Publication (IPP) 2015: 0.333

Mathematical Citation Quotient (MCQ) 2015: 0.33

Online
ISSN
1869-6090
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Harmonic analysis and generalized functional equations for the cosine

Driss Zeglami
  • Department of Mathematics, ENSAM, Moulay Ismaïl University, BP 15290, Al Mansour, Meknès, Morocco
  • :
/ Brahim Fadli
  • Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 14000, Kenitra, Morocco
  • :
/ Samir Kabbaj
  • Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 14000, Kenitra, Morocco
  • :
Published Online: 2015-08-12 | DOI: https://doi.org/10.1515/apam-2015-0040

Abstract

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


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, August 2015

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