Recovering Banach-valued coefficients of series with respect to characters of zero-dimensional groups

Abstract. Henstock type integrals for Banach-space-valued functions on zero-dimensional compact abelian group are introduced and used to recover, by generalized Fourier formulae, the vector-valued coefficients of series with respect to characters of such a group. The problem of convergence of Fourier-Henstock series is also investigated.

Key words and phrases. Zero-dimensional abelian group, characters of the group, Banach-space-valued functions, Henstock type integrals, Variational Henstock integral, Henstock–Pettis integral, differentiation with respect to a basis, Fourier–Henstock series.