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.


43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A35 Positive definite functions on groups, semigroups, etc.
Full Text: DOI


[1] DOI: 10.4064/cm108-2-8 · Zbl 1274.42018
[2] DOI: 10.1080/10652460802091500 · Zbl 1158.43005
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