Aarhus University Seal / Aarhus Universitets segl

d'Alembert's other functional equation

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

DOI

  • Bruce Ebanks, Mississippi State Univ, Mississippi State University, Dept Math & Stat
  • ,
  • Henrik Stetkaer

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

Se relationer på Aarhus Universitet Citationsformater

ID: 96029136