On Kurzweil-Stieltjes integral in a Banach space

Title:

On Kurzweil-Stieltjes integral in a Banach space

Creator:

Monteiro, Giselle A. and Tvrdý, Milan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:4a0a3c7f-9b43-4c3a-b9de-fa72d8cbbae7
uuid:4a0a3c7f-9b43-4c3a-b9de-fa72d8cbbae7
doi:10.21136/MB.2012.142992

Subject:

Kurzweil-Stieltjes integral, substitution formula, and integration-by-parts

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space X. We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral ∫ b a d[F]g exists if F : [a, b] → L(X) has a bounded semi-variation on [a, b] and g : [a, b] → X is regulated on [a, b]. We prove that this integral has sense also if F is regulated on [a, b] and g has a bounded semi-variation on [a, b]. Furthermore, the integration by parts theorem is presented under the assumptions not covered by Schwabik (2001) and Naralenkov (2004), and the substitution formula is proved.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

365-381

Source:

Mathematica bohemica | 2012 Volume:137 | Number:4

Harvested from:

CDK

Metadata only:

false