Aarhus University Seal

d'Alembert's other functional equation

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


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).

Original languageEnglish
Article number6
JournalPublicationes mathematicae-Debrecen
Pages (from-to)319-349
Number of pages31
Publication statusPublished - 2015

    Research areas

  • Functional equation, d'Alembert, group, compact group, irreducible representation

See relations at Aarhus University Citationformats

ID: 96029136