0000000000220881
AUTHOR
V. A. Skvortsov
P-adic Henstock integral in the problem of representation of functions by multiplicative transforms
We 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.
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
Abstract A 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.
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
The 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.
Integration of both the derivatives with respect to P-paths and approximative derivatives
In 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.
On Descriptive Characterizations of an Integral Recovering a Function from Its $$L^r$$-Derivative
The 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 classes