Search results for "Henstock-Kurzweil"
showing 4 items of 14 documents
THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL
2022
We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.
Decomposability in the space of HKP-integrable functions
2014
In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.
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.
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.