Substitution formulas for the Kurzweil and Henstock vector integrals

Title:

Substitution formulas for the Kurzweil and Henstock vector integrals

Creator:

Federson, M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:35f9a405-5de3-4b58-b0c8-ec158e62da5a
uuid:35f9a405-5de3-4b58-b0c8-ec158e62da5a
doi:10.21136/MB.2002.133979

Subject:

Kurzweil-Henstock integrals, integration by parts, and integration by substitution

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and prove Substitution Formulas by functional analytic methods. In general, Substitution Formulas need not hold for Kurzweil vector integrals even if they are defined.

Language:

English

Rights:

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

Coverage:

15-26

Source:

Mathematica bohemica | 2002 Volume:127 | Number:1

Harvested from:

CDK

Metadata only:

false