Regulated functions and the Perron-Stieltjes integral

Milan Tvrdý

Časopis pro pěstování matematiky (1989)

  • Volume: 114, Issue: 2, page 187-209
  • ISSN: 0528-2195

How to cite

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Tvrdý, Milan. "Regulated functions and the Perron-Stieltjes integral." Časopis pro pěstování matematiky 114.2 (1989): 187-209. <http://eudml.org/doc/19543>.

@article{Tvrdý1989,
author = {Tvrdý, Milan},
journal = {Časopis pro pěstování matematiky},
keywords = {Banach space of regulated functions; Dushnik-Stieltjes integral; Perron-Stieltjes integral; Kurzweil's theory; integration by parts theorem; substitution theorem; generalized differential equations; Volterra-Stieltjes integral equations},
language = {eng},
number = {2},
pages = {187-209},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {Regulated functions and the Perron-Stieltjes integral},
url = {http://eudml.org/doc/19543},
volume = {114},
year = {1989},
}

TY - JOUR
AU - Tvrdý, Milan
TI - Regulated functions and the Perron-Stieltjes integral
JO - Časopis pro pěstování matematiky
PY - 1989
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 114
IS - 2
SP - 187
EP - 209
LA - eng
KW - Banach space of regulated functions; Dushnik-Stieltjes integral; Perron-Stieltjes integral; Kurzweil's theory; integration by parts theorem; substitution theorem; generalized differential equations; Volterra-Stieltjes integral equations
UR - http://eudml.org/doc/19543
ER -

References

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  1. G. Aumann, Reelle Funktionen, Springer-Verlag, Berlin-Heidelberg-New York, 1969. (1969) Zbl0181.05801MR0061652
  2. D. Fraňková, Regulated functions, to appear. MR1100424
  3. D. Fraňková, Continuous dependence on a parameter of solutions of generalized differential equations, to appear. MR1016632
  4. T. H. Hildebrandt, Introduction to the Theory of Integration, Academic Press, New York-London, 1963. (1963) Zbl0112.28302MR0154957
  5. Ch. S. Hönig, Volterra Stieltjes-Integral Equations, Mathematics Studies 16, North-Holland, Amsterdam, 1975. (1975) MR0499969
  6. Ch. S. Hönig, Volterra Stieltjes-Integral Equations, Functional Differential Equations and Bifurcation, Proceedings of the Sao Carlos Conference 1979, Springer Lecture Notes in Mathematics 799, 173-216. (1979) MR0585488
  7. H. S. Kaltenborn, Linear functional operations on functions having discontinuities of the first kind, Bulletin A.M.S. 40 (1934), 702-708. (1934) Zbl0010.16905MR1562957
  8. I. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (82) (1957), 418-449. (1957) Zbl0090.30002MR0111875
  9. I. Kurzweil, Nichtabsolut konvergente Integrate, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. (1980) 
  10. S. Saks, Theory of the Integral, Monografie Matematyczne, Warszawa-Lwow, 1937. (1937) Zbl0017.30004
  11. Š. Schwabik, Generalized Differential Equations, (Fundamental results), Rozpravy Československé akademie věd, řada matematických a přírodních věd, 95 (6), Academia, Praha, 1985. (1985) Zbl0594.34002MR0823224
  12. Š. Schwabik, On the relation between Young's and Kurzweil's concept of Stieltjes integral, Časopis pěst. mat. 98 (1973), 237-251. (1973) Zbl0266.26006MR0322113
  13. Š. Schwabik, On modified sum integral of Stieltjes type, Časopis pěst. mat. 98 (1973), 274-277. (1973) MR0322114
  14. Š. Schwabik M. Tvrdý, O. Vejvoda, Differential and Integral Equations: Boundary Value Problems and Adjoints, Academia, Praha and D. Reidel, Dordrecht, 1979. (1979) MR0542283
  15. A. J. Ward, The Perron-Stieltjes integral, Math. Zeitschr. 41 (1936), 578-604. (1936) Zbl0014.39702MR1545641

Citations in EuDML Documents

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  1. Štefan Schwabik, Linear operators in the space of regulated functions
  2. Pavel Krejčí, Matthias Liero, Rate independent Kurzweil processes
  3. Pavel Krejčí, Jaroslav Kurzweil, A nonexistence result for the Kurzweil integral
  4. Pavel Krejčí, Harbir Lamba, Giselle Antunes Monteiro, Dmitrii Rachinskii, The Kurzweil integral in financial market modeling
  5. Pavel Krejčí, The Kurzweil integral with exclusion of negligible sets
  6. Milan Tvrdý, Linear distributional differential equations of the second order
  7. Martin Pelant, Milan Tvrdý, Linear distributional differential equations in the space of regulated functions
  8. Giselle A. Monteiro, Milan Tvrdý, On Kurzweil-Stieltjes integral in a Banach space
  9. Milan Tvrdý, Linear integral equations in the space of regulated functions
  10. Milan Tvrdý, Generalized differential equations in the space of regulated functions (boundary value problems and controllability)

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