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aequationes mathematicae

, Volume 67, Issue 1–2, pp 188–194 | Cite as

Applications of Wilson’s functional equation

  • Pavlos Sinopoulos
Research paper
  • 36 Downloads

Summary.

We reduce the functional equation

\( f(x + y) - f(x - y) = \sum_{i=1}^{n} g_{i}(x)h_{i}(y) \)

for n = 1, 2, 3 to the matrix equation

\( E(x + y) + E(x - y) = [E(y) + E(-y)]E(x) \)

and we determine the general solutions for n = 2.

Mathematics Subject Classification (2000).

39B42 39B52 39B72. 

Keywords.

Wilson’s functional equation Vector-valued function Matrix-valued function Abelian group. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  • Pavlos Sinopoulos
    • 1
    • 2
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece
  2. 2.AthensGreece

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