Henstock-Kurzweil and McShane product integration; descriptive definitions
Antonín Slavík; Štefan Schwabik
Czechoslovak Mathematical Journal (2008)
- Volume: 58, Issue: 1, page 241-269
- ISSN: 0011-4642
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topSlavík, Antonín, and Schwabik, Štefan. "Henstock-Kurzweil and McShane product integration; descriptive definitions." Czechoslovak Mathematical Journal 58.1 (2008): 241-269. <http://eudml.org/doc/31209>.
@article{Slavík2008,
abstract = {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 $[a,b]$.},
author = {Slavík, Antonín, Schwabik, Štefan},
journal = {Czechoslovak Mathematical Journal},
keywords = {Henstock-Kurzweil product integral; McShane product integral; Bochner product integral; Henstock-Kurzweil product integral; McShane product integral; Bochner product integral},
language = {eng},
number = {1},
pages = {241-269},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Henstock-Kurzweil and McShane product integration; descriptive definitions},
url = {http://eudml.org/doc/31209},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Slavík, Antonín
AU - Schwabik, Štefan
TI - Henstock-Kurzweil and McShane product integration; descriptive definitions
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 241
EP - 269
AB - 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 $[a,b]$.
LA - eng
KW - Henstock-Kurzweil product integral; McShane product integral; Bochner product integral; Henstock-Kurzweil product integral; McShane product integral; Bochner product integral
UR - http://eudml.org/doc/31209
ER -
References
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- Bochner product integration, Math. Bohem. 119 (1994), 305–335. (1994) Zbl0830.28006MR1305532
- The Perron product integral and generalized linear differential equations, Časopis pěst. mat. 115 (1990), 368–404. (1990) Zbl0724.26006MR1090861
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