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Fourier transforms of vector-valued measures on a certain compact semigroup. (English) Zbl 1023.28006
In this paper some necessary conditions for a Banach space-valued function to be the Fourier transform of a suitable measure are given. Moreover, a sufficient condition for weak compactness of suitable operators is given and, using this result, a sufficient condition for a Banach space-valued function to be the Fourier transform of a regular measure is demonstrated.
MSC:
28B05 Vector-valued set functions, measures and integrals
43A05 Measures on groups and semigroups, etc.
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
47B07 Linear operators defined by compactness properties
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