Francesco Tulone

Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group

Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.

On the Coefficients of Multiple Series with Respect to Vilenkin System

Abstract We give a sufficient condition for coefficients of double series Σ Σn,m an,m χn,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.

Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space

ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.

Inversion formulae for the integral transform on a locally compact zero-dimensional group

Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.

Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.