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Title: A note on integration by parts for abstract Perron-Stieltjes integrals (English)
Author: Schwabik, Štefan
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 126
Issue: 3
Year: 2001
Pages: 613-629
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: integration by parts
Keyword: Kurzweil-Stieltjes integral
Keyword: Perron-Stieltjes integral
MSC: 26A39
idZBL: Zbl 0980.26005
idMR: MR1970264
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Date available: 2009-09-24T21:55:00Z
Last updated: 2012-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/134198
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Reference: [1] Henstock, R.: Integration by parts.Aequationes Mathematicae 9 (1973), 1–18. Zbl 0257.26002, MR 0315059
Reference: [2] Hönig, Ch. S.: Volterra Stieltjes-Integral Equations.North-Holland Publ. Comp., Amsterdam, 1975. MR 0499969
Reference: [3] Kurzweil, J.: On integration by parts.Czechoslovak Math. J. 8 (1958), 356–359. Zbl 0094.03505, MR 0111877
Reference: [4] Kurzweil, J.: Nichtabsolut konvergente Integrale.BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. Zbl 0441.28001, MR 0597703
Reference: [5] Schwabik, Š.: Abstract Perron-Stieltjes integral.Math. Bohem. 121 (1996), 425–447. Zbl 0879.28021, MR 1428144
Reference: [6] Schwabik, Š.: Generalized Ordinary Differential Equations.World Scientific, Singapore, 1992. Zbl 0781.34003, MR 1200241
Reference: [7] Schwabik, Š., Tvrdý, M., Vejvoda O.: Differential and Integral Equations.Academia & Reidel, Praha & Dordrecht, 1979. MR 0542283
Reference: [8] Schwabik, Š.: Linear Stieltjes integral equations in Banach spaces.Math. Bohem. 124 (1999), 433–457. Zbl 0937.34047, MR 1722877
Reference: [9] Schwabik, Š.: Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions.Math. Bohem. 125 (2000), 431–454. Zbl 0974.34057, MR 1802292
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