Geodesic
The dual of the space of functions of bounded variation
Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 1-9

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.2006.134078
Classification : 26A39, 26A42, 26A45, 46B26, 46E99
Keywords: bounded variation; two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function 
Aye, Khaing Khaing; Lee, Peng Yee. The dual of the space of functions of bounded variation. Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 1-9. doi: 10.21136/MB.2006.134078
@article{10_21136_MB_2006_134078,
     author = {Aye, Khaing Khaing and Lee, Peng Yee},
     title = {The dual of the space of functions of bounded variation},
     journal = {Mathematica Bohemica},
     pages = {1--9},
     year = {2006},
     volume = {131},
     number = {1},
     doi = {10.21136/MB.2006.134078},
     mrnumber = {2210998},
     zbl = {1112.26008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134078/}
}
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
SP  - 1
EP  - 9
VL  - 131
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134078/
DO  - 10.21136/MB.2006.134078
LA  - en
ID  - 10_21136_MB_2006_134078
ER  - 
%0 Journal Article
%A Aye, Khaing Khaing
%A Lee, Peng Yee
%T The dual of the space of functions of bounded variation
%J Mathematica Bohemica
%D 2006
%P 1-9
%V 131
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134078/
%R 10.21136/MB.2006.134078
%G en
%F 10_21136_MB_2006_134078

[1] D. Franková: Regulated functions. Math. Bohem. 116 (1991), 20–59. | MR

[2] J. Dieudonné: Foundations of Modern Analysis. New-York, 1960. | MR

[3] K. K. Aye: The duals of some Banach spaces. Ph.D Thesis, Nanyang Technological University, 2002.

[4] M. Tvrdý: Linear bounded functionals on the space of regular regulated functions. Tatra Mt. Math. Publ. 8 (1996), 203–210. | MR

[5] P. Habala, P. Hájek, V. Zizler: Introduction to Banach Spaces. 1996.

[6] P. Y. Lee: Lanzhou Lectures on Henstock Integration. World Scientific, 1989. | MR | Zbl

[7] P. Y. Lee, R. Výborný: The Integral: An Easy Approach after Kurzweil and Henstock. Cambridge University Press, 2000. | MR

[8] T. H. Hildebrandt: Introduction of the Theory of Integration. Academic Press, 1963. | MR

[9] T. H. Hildebrandt: Linear continuous functionals on the space (BV) with weak topologies. Proc. Amer. Math. Soc. 17 (1966), 658–664. | MR | Zbl

[10] Tom M. Apostol: Mathematical Analysis. 1957.

[11] W. Orlicz: Linear Functional Analysis. World Scientific, 1992. | MR | Zbl

[12] K. K. Aye, P. Y. Lee: Orthogonally additive functionals on BV. Math. Bohem. 129 (2004), 411–419. | MR

[13] Š. Schwabik: A survey of some new results for regulated functions. Seminario Brasileiro de analise 28 (1988).

[14] M. Brokate, P. Krejčí: Duality in the space of regulated functions and the play operator. Math. Z. 245 (2003), 667–668. | DOI | MR

Cité par Sources :