Аннотация:A variational version of a Henstock type integral with respect to an abstract derivation basis in a topological measure space is defined for the
case of Banach space-valued integrands. It is shown that this integral recovers a primitive from its derivative which is defined with respect to
the same basis.
As an example of an application of this theory in harmonic analysis, a derivation bases and the respective Henstock type integrals on a zero-dimensional group are considered. It is shown that the variational integral on such a group solves the problem of recovering, by generalized Fourier formulas, the Banach space-valued coefficients of a
series with respect to characters of this group
