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Start Over Creator Schwabik, Štefan Data provider Academy of Sciences Library/Knihovna Akademie věd ČR

23. Henstock-Kurzweil and McShane product integration; descriptive definitions

Creator:
Slavík, Antonín and Schwabik, Štefan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Henstock-Kurzweil product integral, McShane product integral, and Bochner product integral
Language:
English
Description:
The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function $A$ is absolutely continuous. As a consequence we obtain that the McShane product integral of $A$ over $[a,b]$ exists and is invertible if and only if $A$ is Bochner integrable on $[a,b]$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public