Applications of Wilson's functional equation

Author: Sinopoulos, Pavlos

Source: aequationes mathematicae, Volume 67, Numbers 1-2, March 2004 , pp. 188-194(7)

Publisher: Springer

Price: $47.00 plus tax (Refund Policy)

Abstract:

We reduce the functional equation

<MediaObject> </MediaObject> $$ f(x + y) - f(x - y) = \sum_{i=1}^{n} g_{i}(x)h_{i}(y) $$

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

<MediaObject> </MediaObject> $$ E(x + y) + E(x - y) = [E(y) + E(-y)]E(x) $$

and we determine the general solutions for n = 2.

Keywords: 39B42; 39B52; 39B72; Wilson's functional equation; Vector-valued function; Matrix-valued function; Abelian group

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s00010-003-2704-8

Affiliations: 1: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece,

Publication date: 2004-03-01

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