| Title:
|
A note on integration by parts for abstract Perron-Stieltjes integrals (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
613-629 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.2001.134198 |
| . |
| Date available:
|
2009-09-24T21:55:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134198 |
| . |
| Reference:
|
[1] Henstock, R.: Integration by parts.Aequationes Mathematicae 9 (1973), 1–18. Zbl 0257.26002, MR 0315059, 10.1007/BF01838184 |
| 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 |
| . |
