논문KCI 등재
A FRESNEL TYPE CLASS ON FUNCTION SPACE
한국수학교육학회|2009.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제16권 제1호|pp. 107-119
2
조회
0
다운로드
2
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.
Abstract
In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.
참고문헌 (13)
- S. Albeverio, "Mathematical theory of Feynman path integrals. Lec- ture Notes in Mathematics, 523" (1976), Springer-Verlag
- R.H. Cameron, "Some Banach algebras of analytic Feynman integrable functionals. Analytic Functions (Kozubnik, 1979), Lecture Notes in Mathematics, 798", pp.18~67 (1980), Springer
- S.J. Chang, "Conditional function space integrals with applications", Rocky Mountain J. Math, 26, pp.37~62 (1996)
- S.J. Chang, "The partial di®erential equation on function space with respect to an integral equation", J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math, 4, pp.47~60 (1997)
- S.J. Chang, "Generalized Fourier-Feynman transforms and a ¯rst variation on function space", Integral Transforms and Special Functions, 14, pp.375~393 (2003)
- L. Gross, "Abstract Wiener space", Proc. 5th Berkeley Sym. on Math. Stat. Prob, 2, pp.31~42 (1965)
- G.W. Johnson, "An unsymmetric Fubini theorem", Amer. Math. Monthly, 91, pp.131~133 (1984)
- G.W. Johnson, "Notes on the Feynman integral, III: The Schroedinger equation", Paci¯c J. Math, 105, pp.321~358 (1983)
- G. Kallianpur, "Generalized Feynman integrals using analytic continua-tion in several complex variables. Stochastic Analysis and Applications" (1984), Marcel Dekker, Inc
- G. Kallianpur, "Analytic and sequential Feynman in- tegrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula", Ann.Inst. Henri Poincare, 21, pp.323~361 (1985)
- H.-H. Kuo, "Gaussian measure in Banach spaces. Lecture Notes in Mathematics, 463" (1975), Springer
- J. Yeh, "Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments. Illinois", J. Math, 15, pp.37~46 (1971)
- J. Yeh, "Stochastic Processes and the Wiener Integral" (1973), Marcel Dekker, Inc
관련 논문AI추천
Generalized analytic Fourier-Feynman transforms and convolutions on a Fresnel type class이일용, 장승준대한수학회 · 대한수학회보2011 · 제48권 제2호A Banach algebra and its equivalent spaces over paths with a positive measure조동현대한수학회 · 대한수학회논문집2020 · 제35권 제3호Conditional generalized Fourier-Feynman transform of functionals in a Fresnel type class장승준대한수학회 · 대한수학회논문집2011 · 제26권 제2호Shifting and modulation for the convolution product of functionals in a generalized Fresnel class김병수, 박연희강원경기수학회 · 한국수학논문집2018 · 제26권 제3호Shifting and modulation for Fourier-Feynman transform of functionals in a generalized Fresnel class김병수강원경기수학회 · 한국수학논문집2017 · 제25권 제3호A Banach algebra of series of functions over paths권모아, 조동현강원경기수학회 · 한국수학논문집2019 · 제27권 제2호
이 간행물의 다른 논문 (13건)
BCK-ALGEBRAS WITH SUPREMUM박철환, 이경자, 전영배pp. 1-11ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyrospp. 13-18SOME COMMON FIXED POINT THEOREMS USING COMPATIBLE MAPS OF TYPE(α) ON INTUITIONISTIC FUZZY METRIC SPACE박종서pp. 19-30EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS OF CODIMENSION 2진대호pp. 31-46ON THE PARALLELOGRAM LAW AND BOHR'S INEQUALITY IN G-INNER PRODUCT SPACES조열제, Josip Pecaric, Vera Culjakpp. 47-57