Concrete algebraic cohomology for the group (â„, +) or how to solve the functional equation ð‘“(ð‘¥+ð‘¦) - ð‘“(ð‘¥) - ð‘“(ð‘¦) = ð‘”(ð‘¥, ð‘¦)
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Mihai Prunescu
mihai.prunescu@math.uni-freiburg.de
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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.
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Published
2007-12-01
How to Cite
[1]
M. Prunescu, “Concrete algebraic cohomology for the group (â„, +) or how to solve the functional equation ð‘“(ð‘¥+ð‘¦) - ð‘“(ð‘¥) - ð‘‘(ð‘¦) = ð‘’(ð‘¥, ð‘¦)”, CUBO, vol. 9, no. 3, pp. 39–45, Dec. 2007.
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