112,678 research outputs found
Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
No full textsummary: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
Erratum to: Integration by Parts for Perron Type Integrals of Order 1 and 2 in Riesz Spaces
No full textThe proof of differentiability of the integral function I2 in
[Boccuto-Sambucini-Skvortsov, Integration by Parts for Perron Type Integrals of Order 1 and 2 in Riesz Spaces, Theorem 7.9]
is based on the sufficient condition for global differentiability;
given in the paper
Boccuto, A., Skvortsov, V.A.: Remark on the Maeda–Ogasawara–Vulikh representation theorem for Riesz spaces and applications to Differential Calculus. Acta Math. (Nitra) 9, 13–24 (2006).
thes statement given in that paper is not justified in properly. In fact the following question seems to be open: if the “componentwise differentiability” in the complement of a meager set does imply global differentiability, where the involved “components” are taken according to the Maeda–Ogasawara–Vulikh representation theorem for Riesz spaces.
To overcome this gap we present here a new proof of differentiability of the integral function I2
Perron type integral on compact zero-dimensional Abelian groups
No full textPerron 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
Multidimensional P-adic Integrals in some Problems of Harmonic Analysis
No full textThe 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
Generalized Henstock integrals in the theory of series in multiplicative systems
No full textProperties 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-Kurzweil type integrals on zero-dimensional groups and its application in harmonic analysis
No full textIntegration of both the derivatives with respect to P-paths and approximative derivatives
No full textIn the present paper, in terms of generalized absolute continuity, we present a descriptive characteristic of the primitive with respect to a system of P-paths and study the relationship between the Denjoy-Khinchin integral and the Henstock H P-integral. © 2009 Pleiades Publishing, Ltd
Representation of quasi-measure by a Henstock-Kurzweil type integral on a compact zero-dimensional metric space
No full textA 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
Henstock-Kurzweil type integrals on zero-dimensional groups and its application in Harmonic Analysis
No full textWe introduce here a Henstock type integral on compact subsets of a locally compact zero-dimensional abelian group and we use this integral to solve the problem of recovering the coefficients of convergent series with respect to characters of a compact zero dimensional abelian group and to obtain an inversion formula for multiplicative integral transform with a kernel expressed in terms of characters of a locally compact zero dimensional abelian group
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