On summability, multipliability, product integrability, and parallel translation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333135" target="_blank" >RIV/00216208:11320/16:10333135 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2015.07.043" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2015.07.043</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2015.07.043" target="_blank" >10.1016/j.jmaa.2015.07.043</a>

Result language
angličtina
Original language name
On summability, multipliability, product integrability, and parallel translation
Original language description
In this paper we provide necessary and sufficient conditions for the existence of the Kurzweil, McShane and Riemann product integrals of step mappings with well-ordered steps, and for right regulated mappings with values in Banach algebras. Our basic tools are the concepts of summability and multipliability of families in normed algebras indexed by well-ordered subsets of the real line. These concepts also lead to the generalization of some results from the usual theory of infinite series and products. Finally, we present two applications of product integrals: First, we describe the relation between Stieltjes-type product integrals, Haahti products, and parallel translation operators. Second, we provide a link between the theory of strong Kurzweil product integrals and strong solutions of linear generalized differential equations.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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