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Fourier transform of Radon measures on a locally compact group. (English) Zbl 1247.43005
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:
43A25Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A35Positive definite functions on groups, semigroups, etc.