A note on integration by parts for abstract Perron-Stieltjes integrals

Štefan Schwabik

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 3, page 613-629
  • ISSN: 0862-7959

Abstract

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Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.

How to cite

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Schwabik, Štefan. "A note on integration by parts for abstract Perron-Stieltjes integrals." Mathematica Bohemica 126.3 (2001): 613-629. <http://eudml.org/doc/248861>.

@article{Schwabik2001,
abstract = {Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.},
author = {Schwabik, Štefan},
journal = {Mathematica Bohemica},
keywords = {integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral; integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral},
language = {eng},
number = {3},
pages = {613-629},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on integration by parts for abstract Perron-Stieltjes integrals},
url = {http://eudml.org/doc/248861},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Schwabik, Štefan
TI - A note on integration by parts for abstract Perron-Stieltjes integrals
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 613
EP - 629
AB - Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.
LA - eng
KW - integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral; integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral
UR - http://eudml.org/doc/248861
ER -

References

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  1. 10.1007/BF01838184, Aequationes Mathematicae 9 (1973), 1–18. (1973) Zbl0257.26002MR0315059DOI10.1007/BF01838184
  2. Volterra Stieltjes-Integral Equations, North-Holland Publ. Comp., Amsterdam, 1975. (1975) MR0499969
  3. On integration by parts, Czechoslovak Math. J. 8 (1958), 356–359. (1958) Zbl0094.03505MR0111877
  4. Nichtabsolut konvergente Integrale, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
  5. Abstract Perron-Stieltjes integral, Math. Bohem. 121 (1996), 425–447. (1996) Zbl0879.28021MR1428144
  6. Generalized Ordinary Differential Equations, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
  7. Differential and Integral Equations, Academia & Reidel, Praha & Dordrecht, 1979. (1979) MR0542283
  8. Linear Stieltjes integral equations in Banach spaces, Math. Bohem. 124 (1999), 433–457. (1999) Zbl0937.34047MR1722877
  9. Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions, Math. Bohem. 125 (2000), 431–454. (2000) Zbl0974.34057MR1802292

Citations in EuDML Documents

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  1. Boonpogkrong Varayu, Tuan-Seng Chew, The Henstock-Kurzweil approach to Young integrals with integrators in BV φ
  2. Štefan Schwabik, Operator-valued functions of bounded semivariation and convolutions
  3. Giselle A. Monteiro, Milan Tvrdý, On Kurzweil-Stieltjes integral in a Banach space
  4. Umi Mahnuna Hanung, Milan Tvrdý, On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil
  5. Umi Mahnuna Hanung, Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

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