The expected value of the line integral of one-forms
type: Item
instance of: scholarly article
title: The expected value of the line integral of one-forms
zbMATH Open document ID: 1118.26010
published in: Bulletin des Sciences Mathématiques
publication date: 2007-02-14T00:00:00Z
review text: The author analyses from the point of view of measure theory the problem of approximating a line integral using the quotient of Newton instead of the derivative. It is demonstrated that the expected value of a certain scheme of approximation of line integrals of closed one-form \(\beta\), with respect to the Wiener measure, converges to the integral over the interval of the parameter, of the expected value of the adjoint \(\delta\) of the exterior derivative, applied to the one-form. Another result is that if the denominator of the quotient of Newton is risen to a power smaller than \(1/2\), and if the line integral of a harmonic form is approximated by using this new quotient, then for almost all continuous lines, the inferior limit of this scheme of approximation is zero.
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 5126089
zbMATH Keywords: measure theory
zbMATH Keywords: quotient of Newton
zbMATH Keywords: Wiener measure
author: J. L. Martínez Morales
reviewed by: Octavian Lipovan
MaRDI profile type: Publication
full work available at URL: j.bulsci.2006.03.007
OpenAlex ID: W2048653935
cites work: Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
cites work: Q3364873
cites work: Q4339232
cites work: The Laplacian on a Riemannian manifold. An introduction to analysis on manifolds
cites work: Q3138776
DOI: 10.1016/J.BULSCI.2006.03.007
description: scientific article; zbMATH DE number 5126089