Bochner product integration

Štefan Schwabik

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 3, page 305-335
  • ISSN: 0862-7959

Abstract

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A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].

How to cite

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Schwabik, Štefan. "Bochner product integration." Mathematica Bohemica 119.3 (1994): 305-335. <http://eudml.org/doc/29316>.

@article{Schwabik1994,
abstract = {A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].},
author = {Schwabik, Štefan},
journal = {Mathematica Bohemica},
keywords = {Kurzweil-Henstock integral; Bochner integral; product integral; Bochner product integral; Kurzweil-Henstock integral; Bochner integral; product integral},
language = {eng},
number = {3},
pages = {305-335},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bochner product integration},
url = {http://eudml.org/doc/29316},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Schwabik, Štefan
TI - Bochner product integration
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 3
SP - 305
EP - 335
AB - A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].
LA - eng
KW - Kurzweil-Henstock integral; Bochner integral; product integral; Bochner product integral; Kurzweil-Henstock integral; Bochner integral; product integral
UR - http://eudml.org/doc/29316
ER -

References

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  12. E. J. McShane, Unified Integration, Academic Press, New York, London, 1983. (1983) Zbl0551.28001MR0740710
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  16. Š. Schwabik, The Perron product integral and generalized linear differential equations, Časopis pěst. mat. 115 (1990), 368-404. (1990) Zbl0724.26006MR1090861
  17. Š. Schwabik, Generalized Ordinary Differential Equations, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
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