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Advances in Pure and Applied Mathematics

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1869-6090
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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
  • Email:
/ Brahim Fadli
  • Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 14000, Kenitra, Morocco
  • Email:
/ Samir Kabbaj
  • Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 14000, Kenitra, Morocco
  • Email:
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

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, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2015-0040. Export Citation

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