논문KCI 등재
Change of scale formulas for function space integrals related with Fourier-Feynman transform and convolution on $C_{a,b}[0,T]$
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra ${\mathcal S}(L_{a,b}^2[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.
Abstract
We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra ${\mathcal S}(L_{a,b}^2[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.
참고문헌 (21)
- R.H. Cameron, "The translation pathology of Wiener space", Duke Math. J, 21, pp.623~628 (1954)
- R.H. Cameron, "The behavior of measure and measurability under change of scale in Wiener space", Bull. Amer. Math. Soc, 53, pp.130~137 (1947)
- R.H. Cameron, "An L2 analytic Fourier-Feynman transform", Michigan Math. J, 23, pp.1~30 (1976)
- R.H. Cameron, "Lecture Notes in Math", pp.18~67 (1980), Springer-Verlag
- R.H. Cameron, "Change of scale formulas for Wiener integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo", Serie II-Numero, 17, pp.105~115 (1987)
- R.H. Cameron, "Relationships between the Wiener integral and the analytic Feynman integral, Supplemento ai Rendiconti del Circolo Matem-atico di Palermo", Serie II-Numero, 17, pp.117~133 (1987)
- 장승준, "Multiple $L_p$ analytic generalized Fourier-Feynman transform onthe Banach algebra", 대한수학회논문집, 19(1), pp.93~111 (2004), 대한수학회
- S.J. Chang, "Integration by parts formulas involving generalized Fourier-Feynman transforms on function space", Trans. Amer. Math. Soc, 355, pp.2925~2948 (2003)
- S.J. Chang, "Generalized Fourier-Feynman transforms and a rst variation on function space", Integral Transform. Spec. Funct, 14, pp.375~393 (2003)
- T. Human, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
- T. Human, "Convolutions and Fourier-Feynman trans-forms of functionals involving multiple integrals", Michigan Math. J, 43, pp.247~261 (1996)
- G.W. Johnson, "An Lp analytic Fourier-Feynman transform", Michigan Math. J, 26, pp.103~127 (1979)
- G.W. Johnson, "Scale-invariant measurability in Wiener space", Paciic J. Math, 83, pp.157~176 (1979)
- B.J. Kim, "Change of scale formulas for Wiener integrals related with Fourier-Feynman transform and convolution", J. Function Spaces, 2014, pp.1~7 (2014)
- J. Yeh, "Convolution in Fourier-Wiener transform", Paciic J. Math, 15, pp.731~738 (1965)
- J. Yeh, "Stochastic processes and the Wiener integral" (1973), Marcel Dekker, Inc.
- "Proc. Amer. Math. Soc", 2013, 2729~2739
- I. Yoo, "A change of scale formula for Wiener integrals on abstract Wiener spaces", Internat. J. Math. Math. Sci, 17, pp.239~248 (1994)
- I. Yoo, "A change of scale formula for Wiener integrals on abstract Wiener spaces II", J. Korean Math. Soc, 31, pp.115~129 (1994)
- 유일, "A change of scale formula for Wiener integrals of unbounded functions II", 대한수학회논문집, 21(1), pp.117~133 (2006), 대한수학회
- I. Yoo, "A change of scale formula for Wiener integrals of unbounded functions", Rocky Mountain J. Math, 34, pp.371~389 (2004)
관련 논문AI추천
Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform유일, 김병수강원경기수학회 · 한국수학논문집2021 · 제29권 제2호Generalized analytic Fourier-Feynman transforms and convolutions on a Fresnel type class이일용, 장승준대한수학회 · 대한수학회보2011 · 제48권 제2호Generalized first variation and generalized sequential Fourier-Feynman transform김병수강원경기수학회 · 한국수학논문집2023 · 제31권 제4호Generalized Fourier–Feynman Transform of Bounded Cylinder Functions on the Function Space C_(a,b)[0, T]최재길경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제2호FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FOURIER-TYPE FUNCTIONALS ON WIENER SPACE김병수영남수학회 · East Asian Mathematical Journal2013 · 제29권 제5호Generalized Fourier-Feynman transform and sequential transforms on function space장승준, 최재길대한수학회 · 대한수학회지2012 · 제49권 제5호