Orthogonally additive functionals on B V

Khaing Aye Khaing; Peng Yee Lee

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 4, page 411-419
  • ISSN: 0862-7959

Abstract

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In this paper we give a representation theorem for the orthogonally additive functionals on the space B V in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.

How to cite

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Khaing, Khaing Aye, and Lee, Peng Yee. "Orthogonally additive functionals on $BV$." Mathematica Bohemica 129.4 (2004): 411-419. <http://eudml.org/doc/249396>.

@article{Khaing2004,
abstract = {In this paper we give a representation theorem for the orthogonally additive functionals on the space $BV$ in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.},
author = {Khaing, Khaing Aye, Lee, Peng Yee},
journal = {Mathematica Bohemica},
keywords = {functional; orthogonally additive functional; two-norm space; function of bounded variation; Henstock integral; Stieltjes integral; functional; orthogonally additive functional; two-norm space; function of bounded variation; Henstock integral; Stieltjes integral},
language = {eng},
number = {4},
pages = {411-419},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Orthogonally additive functionals on $BV$},
url = {http://eudml.org/doc/249396},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Khaing, Khaing Aye
AU - Lee, Peng Yee
TI - Orthogonally additive functionals on $BV$
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 4
SP - 411
EP - 419
AB - In this paper we give a representation theorem for the orthogonally additive functionals on the space $BV$ in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
LA - eng
KW - functional; orthogonally additive functional; two-norm space; function of bounded variation; Henstock integral; Stieltjes integral; functional; orthogonally additive functional; two-norm space; function of bounded variation; Henstock integral; Stieltjes integral
UR - http://eudml.org/doc/249396
ER -

References

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  1. Foundations of Modern Analysis, Academic Press, N. Y., 1960. (1960) MR0120319
  2. Regulated functions, Math. Bohem. 116 (1991), 20–59. (1991) MR1100424
  3. Linear continuous functionals on the space ( B V ) with weak topologies, Proc. Amer. Math. Soc. 17 (1966), 658–664. (1966) Zbl0152.13604MR0193490
  4. Lanzhou Lectures on Henstock Integration, World Scientific, 1989. (1989) Zbl0699.26004MR1050957
  5. The Integral: An Easy Approach after Kurzweil and Henstock, Cambridge University Press, 2000. (2000) MR1756319
  6. Linear Functional Analysis, World Scientific, 1992. (1992) Zbl0799.46002MR1182560
  7. Linear bounded functionals on the space of regular regulated functions, Tatra Mt. Math. Publ. 8 (1996), 203–210. (1996) MR1475282
  8. Trigonometric Series I and II, Cambridge University Press, 1977. (1977) MR0617944

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