851 research outputs found
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
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
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
No full textA Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces
P-adic Henstock integral in the theory of series over systems of characters of zero-dimensional groups.
No full textWe introduce a path integral of Henstock type and use it to obtain inversion formulas for
multiplicative integral transformations. The problem considered is a generalization of the problem of reconstruction of coefficients of a convergent orthogonal series from its sum
Henstock-Kurzweil type integration of Riesz-space-valued functions and applications to Walsh series
No full textSome versions of the Henstock-Kurzweil integral with respect to different derivation bases for functions with values in Dedekind complete Riesz spces are studied. Some versions of the Fundamental Formula of Calculus are proved for these kinds of integrals and some applications to Fourier Analysis and Walsh series are given
The Perron Integral of order k in Riesz Spaces
No full textA Perron-type integral of order k for Riesz space-valued functions is defined in terms of the Peano derivatives. Some fundamental properties of this integral, including an integration by parts formula, are presented. We use the tools of Differential and Integral Calculus in Riesz spaces, the divided differences, the k-convexity and some regularity properties of the major and minor functions involved. We use also the Maeda-Ogasawara-Vulikh Riesz representation theorem
On Descriptive Characterizations of an Integral Recovering a Function from Its -Derivative
No full textThe notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classe
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
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
No full textThe theory of HenstockâKurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas
A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure
No full textWe 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
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