The integral sine addition law.
Keywords:
Functional equation, Sine and cosine addition laws, Character, Borel measureAbstract
In the present paper we determine, in terms of characters and additive functions, the solutions of the integral functional equation for the sine addition law (G f(xyt)dµ(t) = f(x)g(y) + g(x)f(y), x, y ∈ G, where G is a locally compact Hausdorff group and µ is a regular, compactly supported, complex-valued Borel measure on G. Some consequences of this result and an example are presented.References
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