Concrete algebraic cohomology for the group (ℝ, +) or how to solve the functional equation 𝑓(𝑥+𝑦) - 𝑓(𝑥) - 𝑓(𝑦) = 𝑔(𝑥, 𝑦)

Downloads

Abstract

The functional equation ð‘“(ð‘¥+ð‘¦) - ð‘“(ð‘¥) - ð‘“(ð‘¦) = ð‘”(ð‘¥, ð‘¦) has a solution ð‘“ that belongs to C0(â„) if and only if the symmetric cocycle ð‘” belongs to C0(â„2). If the symmetric cocyle ð‘” is recursively approximable, there exists a solution ð‘“ which is recursively approximable also. If ð‘” belongs to C1(â„2) then there exists an integral expression in ð‘” for a solution ð‘“ that belongs to C1(â„), and the same happens for the classes Ck, C∞, analytic and polynomial.

Keywords

Algebraic Cohomology , functional equation , analytic properties
  • Mihai Prunescu Hornecker softwareentwicklung, Freiburg, Germany - Institute of Mathematics of the Romanian Academy, Bucharest, Romania.
  • Pages: 39–45
  • Date Published: 2007-12-01
  • Vol. 9 No. 3 (2007): CUBO, A Mathematical Journal

Downloads

Download data is not yet available.

Published

2007-12-01

How to Cite

[1]
M. Prunescu, “Concrete algebraic cohomology for the group (ℝ, +) or how to solve the functional equation 𝑓(𝑥+𝑦) - 𝑓(𝑥) - 𝑑(𝑦) = 𝑒(𝑥, 𝑦)”, CUBO, vol. 9, no. 3, pp. 39–45, Dec. 2007.

Issue

Vol. 9 No. 3 (2007): CUBO, A Mathematical Journal

Section

Articles