0000000000504601

AUTHOR

V. Skvortsov

showing 5 related works from this author

Multidimensional P-adic Integrals in some Problems of Harmonic Analysis

2017

The paper is a survey of results related to the problem of recovering the coefficients of some classical orthogonal series from their sums by generalized Fourier formulas. The method is based on reducing the coefficient problem to the one of recovering a function from its derivative with respect to an appropriate derivation basis. In the case of the multiple Vilenkin system the problem is solved by using a multidimensional P-adic integral.

rectangular convergencequasi-measureHaar seriePerron P-adic integralWalsh serieHenstock-Kurzweil integralSaks continuityVilenkin serie
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Representation of quasi-measure by a Henstock-Kurzweil type integral on a compact zero-dimensional metric space

2009

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.

Settore MAT/05 - Analisi MatematicaQuasi measure Henstock-Kurzweil integral compact metric space
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Generalized Henstock integrals in the theory of series in multiplicative systems

2004

Properties of a Henstock type integral defined by means of a differential basis generated by P-adic paths ae studied. It is proved that this integral solves the problem of coefficients reconstruction by using generalized Fourier formulas for a series over multiplivative systems.

Henstock type integral P-adic path Fourier coefficients on multiplicative system
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A new full descriptive characterization of Denjoy-Perron integral

1995

It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.

Pure mathematicsHenstock–Kurzweil integralMathematical analysisMeasure (physics)Riemann integralFunction (mathematics)Absolute continuitysymbols.namesakesymbolsAlmost everywhereGeometry and TopologyDaniell integralDifferentiable functionAnalysisMathematics
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On the problem of recovering the coefficients of series with respect to characters of zero-dimensional groups

2006

It is proved that if a series with respect to the characters of abelian compact zero-dimensional group is convergent everywhere except, possibly, a countable number of points, then the coefficients of this series can be recovered from its sum by generalized Fourier formulas in which a Henstock-Kurzweil type integral is used.

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