0000000000179446
AUTHOR
Valentin A. Skvortsov
showing 12 related works from this author
Henstock type integral in compact zero-dimensional metric space and quasi-measures representations
2012
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.
Henstock type integral in harmonic analysis on zero-dimensional groups
2006
AbstractA Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.
On the Coefficients of Multiple Series with Respect to Vilenkin System
2017
Abstract We give a sufficient condition for coefficients of double series Σ Σ n,m an,m χ n,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.
Generalized Hake property for integrals of Henstock type
2013
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.
Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series
2015
Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.
Kurzweil-Henstock type integral on zero-dimensional group and some of its application
2008
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.
On Variational Measures Related to Some Bases
2000
Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.
A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
2019
Abstract We introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil–Henstock-type integral related to this basis. We prove a version of Hake’s theorem in terms of a variational measure.
The essential variation of a function and some convergence theorems
1996
ВВОДИтсь ОпРЕДЕлЕНИ Е ВАРИАцИИ ФУНкцИИ, пР И кОтОРОМ ФОРМУлА $$V(F,E) = \int_E {|\bar DF(x)} |dx$$ спРАВЕДлИВА Дль пРОИ жВОльНОИ ФУНкцИИF И пРОИжВОльНОгО ИжМЕР ИМОгО МНОжЕстВАE НА ОтРЕжкЕ пРьМОИ. В т ЕРМИНАх ЁтОИ ВАРИАцИ И пОлУЧЕНы тЕОРЕМы О пОЧлЕННОМ ДИФФЕРЕНцИРОВАНИИ п ОслЕДОВАтЕльНОстИ Ф УНкцИИ И тЕОРЕМы О пРЕДЕльНОМ пЕРЕхОДЕ пОД жНАкОМ И НтЕгРАлА ДАНжУА-пЕРР ОНА.
Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space
2009
Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.
Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group
2009
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.
Perron type integral on compact zero-dimensional Abelian groups
2008
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.