d'Alembert's other functional equation

Bruce Ebanks*, Henrik Stetkaer

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equation

f(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G;

when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact. Some solutions are given by the same formulas as in the known abelian case. The new ones are expressed in terms of matrix-coeffcients of irreducible, 2-dimensional representations of G and of solutions of Wilson's functional equation phi(xy) +phi(xy(-1)) = 2 phi(x)gamma(y).

OriginalsprogEngelsk
Artikelnummer6
TidsskriftPublicationes mathematicae-Debrecen
Vol/bind87
Nummer3-4
Sider (fra-til)319-349
Antal sider31
ISSN0033-3883
DOI
StatusUdgivet - 2015

Fingeraftryk

Dyk ned i forskningsemnerne om 'd'Alembert's other functional equation'. Sammen danner de et unikt fingeraftryk.

Citationsformater