On Wilson’s functional equations

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• 作者：Bruce Ebanks ; Henrik Stetk?r
• 关键词：39B32 ; 39B52 ; Functional equation ; group ; Wilson
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：89
• 期：2
• 页码：339-354
• 全文大小：555 KB
• 参考文献：1.Aczél, J.: Lectures on functional equations and their applications. Math. Sci. Eng. Vol. 19. Academic Press, New York-London (1966). xx+510?pp. 39.00. MR0208210 (34 #8020)
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  15.Yang Dilian: Factorization of cosine functions on compact connected groups. Math. Z. 254(4), 655-74 (2006)View Article MATH MathSciNet
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• 作者单位：Bruce Ebanks (1)
  Henrik Stetk?r (2)
  
  1. Department of Mathematics and Statistics, Mississippi State University, P.O. Drawer MA, Mississippi State, MS, 39762, USA
  2. Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark
  
• 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

We find on a group G the solutions \({f, g:G \to \mathbb{C}}\) of the functional equation \({f(xy) + f(y^{-1}x) = 2f(x)g(y), x, y \in G}\), in terms of characters, additive maps and matrix-elements of irreducible, 2-dimensional representations of G.