Aarhus Universitets segl

The kernel of the second order Cauchy difference on semigroups

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



Let S be a semigroup, H a 2-torsion free, abelian group and C 2f the second order Cauchy difference of a function f: S→ H. Assuming that H is uniquely 2-divisible or S is generated by its squares we prove that the solutions f of C 2f= 0 are the functions of the form f(x) = j(x) + B(x, x) , where j is a solution of the symmetrized additive Cauchy equation and B is bi-additive. Under certain conditions we prove that the terms j and B are continuous, if f is. We relate the solutions f of C 2f= 0 to Fréchet’s functional equation and to polynomials of degree less than or equal to 2.

TidsskriftAequationes Mathematicae
Sider (fra-til)279–288
Antal sider10
StatusUdgivet - 2017

Se relationer på Aarhus Universitet Citationsformater


Ingen data tilgængelig

ID: 107780410