×

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:

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

References:

[1] DOI: 10.4064/cm108-2-8 · Zbl 1274.42018
[2] DOI: 10.1080/10652460802091500 · Zbl 1158.43005
[3] Dieudonné J., Treatise on Analysis (1978)
[4] Folland G. B., A Course in Abstract Harmonic Analysis (1995) · Zbl 0857.43001
[5] Mikusiński P., Japan. J. Math. (N.S.) 9 pp 159– (1983)
[6] Mikusiński P., Methods Appl. Anal. 10 pp 377– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.