On a variant of?μ-Wilson’s functional equation on a locally compact group

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• 作者：D. Zeglami ; B. Fadli ; S. Kabbaj
• 关键词：Primary 39B72 ; 39B32 ; Superstability ; μ ; Wilson’s functional equation ; μ ; d’Alembert’s equation ; μ ; spherical function
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：89
• 期：5
• 页码：1265-1280
• 全文大小：502 KB
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• 作者单位：D. Zeglami (1)
  B. Fadli (2)
  S. Kabbaj (2)
  
  1. Department of Mathematics, E.N.S.A.M, Moulay Ismail University, BP 15290, Al Mansour, Meknes, Morocco
  2. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded and σ-invariant measure. We determine the continuous, bounded and μ-central solutions of the functional equation $$ \int\limits_{G} f(xty)d \mu (t) + \int\limits_{G} f(\sigma (y) tx) d \mu(t) = 2f(x)g(y),\, \quad x,y \in G. $$