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Zbl 1247.43005
Atanasiu, Dragu; Mikusiński, Piotr
Fourier transform of Radon measures on a locally compact group. (English)
[J] Integral Transforms Spec. Funct. 21, No. 11-12, 815-821 (2010). ISSN 1065-2469; ISSN 1476-8291/e

Summary: A space of generalized functions is constructed that allows us to generalize Bochner's theorem so that all Radon measures on a locally compact group are in a one-to-one correspondence with elements of that space of generalized functions. This defines a Fourier transform for all Radon measures on a locally compact group.
MSC 2000:
*43A25 Fourier type transforms on locally compact abelian groups
43A35 Positive definite functions on groups, etc.

Keywords: locally compact groups; positive definite functions; Bochner theorem; pseudoquotients; Boehmians

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