| Title:
|
Operator-valued functions of bounded semivariation and convolutions (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
745-777 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The abstract Perron-Stieltjes integral in the Kurzweil-Henstock sense given via integral sums is used for defining convolutions of Banach space valued functions. Basic facts concerning integration are preseted, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations. (English) |
| Keyword:
|
Kurzweil-Henstock integration |
| Keyword:
|
convolution |
| Keyword:
|
Banach space |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
26A45 |
| MSC:
|
26E20 |
| MSC:
|
45N05 |
| MSC:
|
46G12 |
| idZBL:
|
Zbl 1001.26005 |
| idMR:
|
MR1869466 |
| DOI:
|
10.21136/MB.2001.134117 |
| . |
| Date available:
|
2009-09-24T21:56:41Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134117 |
| . |
| Reference:
|
[1] O. Diekmann, M. Gyllenberg, H. R. Thieme: Perturbing semigroups by solving Stieltjes renewal equations.Differ. Integral Equ. 6 (1993), 155–181. MR 1190171 |
| Reference:
|
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| Reference:
|
[3] N. Dunford, J. T. Schwartz: Linear Operators I.Interscience Publishers, New York, London, 1958. MR 0117523 |
| Reference:
|
[4] Ch. S. Hönig: Volterra-Stieltjes Integral Equations.North-Holland Publ. Comp., Amsterdam, 1975. MR 0499969 |
| Reference:
|
[5] J. Kurzweil: Nichtabsolut konvergente Integrale.BSB B. G. Teubner, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[6] Š. Schwabik: Generalized Ordinary Differential Equations.World Scientific, Singapore, 1992. Zbl 0781.34003, MR 1200241 |
| Reference:
|
[7] Š. Schwabik, M. Tvrdý, O. Vejvoda: Differential and Integral Equations.Academia & Reidel, Praha & Dordrecht, 1979. MR 0542283 |
| Reference:
|
[8] Š. Schwabik: Abstract Perron-Stieltjes integral.Math. Bohem. 121 (1996), 425–447. Zbl 0879.28021, MR 1428144 |
| Reference:
|
[9] Š. Schwabik: Linear Stieltjes integral equations in Banach spaces.Math. Bohem. 124 (1999), 433–457. MR 1722877 |
| Reference:
|
[10] Š. Schwabik: Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions.Math. Bohem. 125 (2000), 431–454. Zbl 0974.34057, MR 1802292 |
| Reference:
|
[11] Š. Schwabik: A note on integration by parts for abstract Perron-Stieltjes integrals.Math. Bohem. 126 (2001), 613–626. Zbl 0980.26005, MR 1970264 |
| . |
