Operator-valued functions of bounded semivariation and convolutions

Štefan Schwabik

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 4, page 745-777
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Schwabik, Štefan. "Operator-valued functions of bounded semivariation and convolutions." Mathematica Bohemica 126.4 (2001): 745-777. <http://eudml.org/doc/248860>.

@article{Schwabik2001,
abstract = {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.},
author = {Schwabik, Štefan},
journal = {Mathematica Bohemica},
keywords = {Kurzweil-Henstock integration; convolution; Banach space; Kurzweil-Henstock integration; convolution; Banach space-valued functions; functions of bounded semivariation},
language = {eng},
number = {4},
pages = {745-777},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Operator-valued functions of bounded semivariation and convolutions},
url = {http://eudml.org/doc/248860},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Schwabik, Štefan
TI - Operator-valued functions of bounded semivariation and convolutions
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 4
SP - 745
EP - 777
AB - 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.
LA - eng
KW - Kurzweil-Henstock integration; convolution; Banach space; Kurzweil-Henstock integration; convolution; Banach space-valued functions; functions of bounded semivariation
UR - http://eudml.org/doc/248860
ER -

References

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  1. Perturbing semigroups by solving Stieltjes renewal equations, Differ. Integral Equ. 6 (1993), 155–181. (1993) MR1190171
  2. Perturbing evolutionary systems by step responses on cumulative outputs, Differ. Integral Equ. 8 (1995), 1205–1244. (1995) MR1325554
  3. Linear Operators I, Interscience Publishers, New York, London, 1958. (1958) MR0117523
  4. Volterra-Stieltjes Integral Equations, North-Holland Publ. Comp., Amsterdam, 1975. (1975) MR0499969
  5. Nichtabsolut konvergente Integrale, BSB B. G. Teubner, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
  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. Abstract Perron-Stieltjes integral, Math. Bohem. 121 (1996), 425–447. (1996) Zbl0879.28021MR1428144
  9. Linear Stieltjes integral equations in Banach spaces, Math. Bohem. 124 (1999), 433–457. (1999) MR1722877
  10. Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions, Math. Bohem. 125 (2000), 431–454. (2000) Zbl0974.34057MR1802292
  11. A note on integration by parts for abstract Perron-Stieltjes integrals, Math. Bohem. 126 (2001), 613–626. (2001) Zbl0980.26005MR1970264

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