The inversion of approximate and dyadic derivatives using an extension of the Henstock integral
type: Item
instance of: scholarly article
title: The inversion of approximate and dyadic derivatives using an extension of the Henstock integral
zbMATH Open document ID: 0723.26005
author: Russell A. Gordon
published in: Real Analysis Exchange
publication date: 1991-01-01T00:00:00Z
review text: A distribution S on [a,b] is a collection of measurable sets \(\{S_ x:\;x\in [a,b]\}\) such that \(x\in S_ x\) and x is a point of density of \(S_ x\). A collection \(\{(x_ i,[c_ i,d_ i]):\;i=1,...,N\}\) of tagged intervals is called a partition, which is S-subordinate to a positive function \(\delta\) if and only if \(\{[c_ i,d_ i]:\;i=1,...,N\}\) is a partition of [a,b], \(d_ i-c_ i<\delta (x_ i)\) and \(x_ i\in [c_ i,d_ i]\) and \(c_ i,d_ i\in S_{x_ i}\) for each i. Using this notion the author has introduced the Henstock-type integral and has proved basic properties of this integral, including S- differentiability almost everywhere. The second part of the paper is devoted to the study of so called dyadic Henstock integral which is defined with the use of families of intervals with dyadic end-points.
reviewed by: Jerzy Niewiarowski
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 4192046
zbMATH Keywords: dyadic derivatives
zbMATH Keywords: Henstock-type integral
zbMATH Keywords: dyadic Henstock integral
MaRDI profile type: Publication
Recommended article: The generalized inverses of differentiation and integration
Recommended article: An extension of the Henrici formula for Laplace transform inversion
Recommended article: Inverse problems for the Cauchy integral formula and the Cauchy integral derivative formulas
Recommended article: Evaluation of \(H\)-function inversion integrals
Recommended article: Q4734280
Recommended article: Q4232832
Recommended article: The inverse of differential operators and an extension of Trefftz method
Recommended article: Q5317969
Recommended article: Method of approximating inverse operators and its applications to the inversion of potential-type integral transforms
Recommended article: Effective estimates for derivatives of inverse functions
description: scientific article; zbMATH DE number 4192046