Concrete algebraic cohomology for the group (โ„, +) or how to solve the functional equation ๐‘“(๐‘ฅ+๐‘ฆ) - ๐‘“(๐‘ฅ) - ๐‘“(๐‘ฆ) = ๐‘”(๐‘ฅ, ๐‘ฆ)
Prunescu, Mihai
CUBO, A Mathematical Journal, Tome 9 (2007), / Harvested from Cubo, A Mathematical Journal
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The functional equationย ๐‘“(๐‘ฅ+๐‘ฆ) - ๐‘“(๐‘ฅ) - ๐‘“(๐‘ฆ) = ๐‘”(๐‘ฅ, ๐‘ฆ) has a solutionย ๐‘“ that belongs to C0(โ„) if and only if the symmetric cocycle ๐‘” belongs toย C0(โ„2). If the symmetric cocyleย ๐‘” is recursively approximable, there exists a solutionย ๐‘“ which is recursively approximable also. Ifย ๐‘” belongs toย C1(โ„2) then there exists an integral expression in ๐‘” for a solutionย ๐‘“ that belongs toย C1(โ„), and the same happens for the classes Ck, Cโˆž, analytic and polynomial.

Publiรฉ le : 2007-12-01
@article{1586,
     title = {Concrete algebraic cohomology for the group (R, +) or how to solve the functional equation f(x+y) - f(x) - f(y) = g(x, y)},
     journal = {CUBO, A Mathematical Journal},
     volume = {9},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1586}
}

Prunescu, Mihai. Concrete algebraic cohomology for the group (โ„, +) or how to solve the functional equation ๐‘“(๐‘ฅ+๐‘ฆ) - ๐‘“(๐‘ฅ) - ๐‘“(๐‘ฆ) = ๐‘”(๐‘ฅ, ๐‘ฆ). CUBO, A Mathematical Journal, Tome 9 (2007) . http://gdmltest.u-ga.fr/item/1586/