Recovering Banach-valued coefficients of series with respect to characters of zero-dimensional groups. (English) Zbl 1438.46052
This paper deals with the problem of recovering, by generalized Fourier formulae, the vector-valued coefficients of series associated to the characters of a zero-dimensional compact abelian group. An elegant solution is described, based on the problem of recovering a primitive in the context of suitable Henstock type generalizations of Bochner and Pettis integrals. The problem of convergence of Fourier-Henstock series is also investigated.
Reviewer: Constantin Niculescu (Craiova)
MSC:
46G10 | Vector-valued measures and integration |
26A39 | Denjoy and Perron integrals, other special integrals |
28B05 | Vector-valued set functions, measures and integrals |
42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
43A25 | Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups |
43A75 | Harmonic analysis on specific compact groups |