The dual of the space of functions of bounded variation

Khaing Khaing Aye; Peng Yee Lee

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 1, page 1-9
  • ISSN: 0862-7959

Abstract

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In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.

How to cite

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Aye, Khaing Khaing, and Lee, Peng Yee. "The dual of the space of functions of bounded variation." Mathematica Bohemica 131.1 (2006): 1-9. <http://eudml.org/doc/249911>.

@article{Aye2006,
abstract = {In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.},
author = {Aye, Khaing Khaing, Lee, Peng Yee},
journal = {Mathematica Bohemica},
keywords = {bounded variation; two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function; two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function},
language = {eng},
number = {1},
pages = {1-9},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The dual of the space of functions of bounded variation},
url = {http://eudml.org/doc/249911},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Aye, Khaing Khaing
AU - Lee, Peng Yee
TI - The dual of the space of functions of bounded variation
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 1
SP - 1
EP - 9
AB - In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.
LA - eng
KW - bounded variation; two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function; two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function
UR - http://eudml.org/doc/249911
ER -

References

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  2. Foundations of Modern Analysis, New-York, 1960. (1960) MR0120319
  3. The duals of some Banach spaces, Ph.D Thesis, Nanyang Technological University, 2002. (2002) 
  4. Linear bounded functionals on the space of regular regulated functions, Tatra Mt. Math. Publ. 8 (1996), 203–210. (1996) MR1475282
  5. Introduction to Banach Spaces, 1996. (1996) 
  6. Lanzhou Lectures on Henstock Integration, World Scientific, 1989. (1989) Zbl0699.26004MR1050957
  7. The Integral: An Easy Approach after Kurzweil and Henstock, Cambridge University Press, 2000. (2000) MR1756319
  8. Introduction of the Theory of Integration, Academic Press, 1963. (1963) MR0154957
  9. Linear continuous functionals on the space (BV) with weak topologies, Proc. Amer. Math. Soc. 17 (1966), 658–664. (1966) Zbl0152.13604MR0193490
  10. Mathematical Analysis, 1957. (1957) 
  11. Linear Functional Analysis, World Scientific, 1992. (1992) Zbl0799.46002MR1182560
  12. Orthogonally additive functionals on BV, Math. Bohem. 129 (2004), 411–419. (2004) MR2102614
  13. A survey of some new results for regulated functions, Seminario Brasileiro de analise 28 (1988). (1988) 
  14. 10.1007/s00209-003-0563-6, Math. Z. 245 (2003), 667–668. (2003) MR2020705DOI10.1007/s00209-003-0563-6

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