 |
 |
 |
 |
 |
 |
Sains Malaysiana 46(12)(2017): 2549–2554 http://dx.doi.org/10.17576/jsm-2017-4612-33 Transformation and Differentiation
of Henstock-Wiener Integrals (Transformasi
dan Pembezaan Kamiran
Henstock-Wiener) VARAYU BOONPOGKRONG1*
& ELVIRA PEDERES DE LARA-TUPRIO2 1Department
of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, 90112,
Thailand 2Mathematics
Department, Ateneo de Manila University
Loyola Hts., Quezon City, 1108, Philippines Diserahkan: 8 November 2016/Diterima:
18 April 2017 ABSTRACT In this paper, transformation
and differentiation of Henstock-Wiener
integrals are discussed. The approach is by Riemann sums. The
idea is more transparent than that of classical Wiener integral. Keywords: Cameron-Martin theorem;
Henstock integral; Henstock-Kurzweil
integral; Wiener integral ABSTRAK Kertas ini membincangkan
transformasi dan
perbezaan kamiran Henstock-Wiener. Pendekatan yang
digunakan ialah congak Riemann. Idea ini lebih telus
berbanding klasik
integral Wiener. Kata kunci: Cameron-Martin theorem; Henstock integral; Henstock-Kurzweil
integral; Wiener integral RUJUKAN
Apostol,
T.M. 1957. Mathematical Analysis.
Boston: Addison-Wesley. Cabral,
E. & Lee, P.Y. 2000-2001. A fundamental
theorem of calculus for the Kurzweil-Henstock
integrals in xxx. Real Analysis Exchange 26: 867-876.
Cameron, R.H. & Martin, W.T. 1944. Transformations of Wiener integrals under translations. Annals
of Mathematics 45(2): 386-396. Chew,
T.S. & Lee, P.Y. 1994. The Henstock-Wiener
integral. Proceeding of Symposium
on Real Analysis (Xiamen 1993). J. Math. Study 27(1):
60-65. Henstock, R. 1988. Lectures
on the Theory of Integration. Singapore: World Scientific.
Kurzweil,
J. 2000. Henstock-Kurzweil
Integration: Its Relation to Topological Vector Spaces. Singapore: World
Scientific. Lee, P.Y. & Výborný, R. 2000. The
Integral: An Easy Approach after Kurzweil and Henstock.
Cambridge: Cambridge University Press. Lu, J. & Lee, P.Y. 1999. The
primitive of Henstock integrable
functions in Euclidean space. Bull. London
Math. Society 31: 173-180. Muldowney, P. 2012. A Modern Theory of Random
Variation With Applications in Stochastic
Calculus, Financial Mathematics, and Feynman Integration. New
York: John Wiley & Sons. Muldowney, P. 1987. A General
Theory of Integration in Function Spaces, including Wiener and
Feynman Integration. Pitman Research
Notes in Mathematics Series. Harlow: Longman. Yang, C.H. 1998. Measure
theory and the Henstock-Wiener integral.
M.Sc. Thesis. NUS (unpublished). Yang, C.H. & Chew, T.S. 1999. On McShane-Wiener integral. Proceeding of International
Mathematics Conference (Manila 1998), Matimyas
Math. 22(2): 39-46. *Pengarang untuk surat-menyurat; email: varayu.b@psu.ac.th
|
|||
|
