Kurzweil-Henstock type integral on zero-dimensional group and some of its applications

A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case. Supported by RFFI-08-01-00669.     

Absolutely continuous variational measures of Mawhin’s type

In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F- and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodym theorem for these measures.     

Generalized Hake property for integrals of henstock type

An integral of Henstock-Kurzweil type is considered relative to an abstract differential basis in a topological space. It is shown that under certain conditions posed onto the basis this integral satisfies the generalized Hake property.     

Henstock type integral in compact zero-dimensional metric space and quasi-measures representations

Properties of a Henstock type integral defined on a compact zero-dimensional metric space are studied. Theorems on integral representation of so-called quasi-measures, i.e., linear functionals on the space of ??polynomials?? defined on the space of the above mentioned type, are obtained.     

Perron type integral on compact zero-dimensional Abelian groups

Perron and Henstock type integrals defined directly on a compact zero-dimensional Abelian group are studied. It is proved that the considered Perron type integral defined by continuous majorants and minorants is equivalent to the integral defined in the same way, but without assumption on continuity of majorants and minorants.