본문 바로가기
KERD
논문KCI 등재

Shifting and modulation for Fourier-Feynman transform of functionals in a generalized Fresnel class

김병수
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2017.09|한국수학논문집 (Korean Journal of Mathematics)|제25권 제3호|pp. 335-347

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

shiftingmodulationanalytic Feynman integralFourier-Feynman transformgeneralized Fresnel calss
주제분류수학

초록

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

Abstract

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

참고문헌 (17)

  1. J.M. Ahn, "Fourier-Feynman transform, con- volution and rst variation", Acta Math. Hungar, 100, pp.215~235 (2003)
  2. S. Albeverio, "Mathematical theory of Feynman path inte-grals" (1976), Springer-Verlag
  3. M. D. Brue, "A functional transform for Feynman integrals similar to the Fourier transform", pp.1972
  4. R.H. Cameron, "An L2 analytic Fourier-Feynman transform", Michigan Math. J, 23, pp.1~30 (1976)
  5. R. H. Cameron, "Analytic Functions Kozubnik 1979", pp.18~67 (1980), Springer-Verlag
  6. R.H. Cameron, "A new translation theorem for the analytic Feynman integral", Rev. Roum. Math. Pures et Appl, 27, pp.937~944 (1982)
  7. K.S. Chang, "Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space", Rocky Mountain J. Math, 30, pp.823~842 (2000)
  8. T. Hu man, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
  9. T. Hu man, "Convolutions and Fourier-Feynman trans-forms of functionals involving multiple integrals", Michigan Math. J., 43, pp.247~261 (1996)
  10. G.W. Johnson, "An Lp analytic Fourier-Feynman transform", Michigan Math. J, 26, pp.103~127 (1979)
  11. G.W. Johnson, "Scale-invariant measurability in Wiener space", Pacific J. Math, 83, pp.157~176 (1979)
  12. G. Kallianpur, "Stochastic Analysis and Applica-tion", pp.219~267 (1984), Marcel-Dekker Inc
  13. G. Kallianpur, "Analytic and sequential Feyn-man integrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula", Ann. Inst. Henri. Poincare, 21, pp.323~361 (1985)
  14. B.S. Kim, "Shifting and variational properties for Fourier-Feynman transform and convolution", J. Funct. Space, 2015, pp.1~9 (2015)
  15. Byoung Soo Kim, "ANALYTIC FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FUNCTIONALS IN A GENERALIZED FRESNEL CLASS", 충청수학회지, 22(3), pp.481~495 (2009), 충청수학회
  16. P.V. O'Neil, "Advanced engineering mathematics" (2003), Thomson
  17. 유일, "Fourier-Feynman transforms for functionals in a generalized Fresnel class", 대한수학회논문집, 22(1), pp.75~90 (2007), 대한수학회

관련 논문AI추천

Shifting and modulation for the convolution product of functionals in a generalized Fresnel class김병수, 박연희강원경기수학회 · 한국수학논문집2018 · 제26권 제3호Generalized analytic Fourier-Feynman transforms and convolutions on a Fresnel type class이일용, 장승준대한수학회 · 대한수학회보2011 · 제48권 제2호Fourier-Feynman transforms for functionals in a generalized Fresnel class유일, 김병수대한수학회 · 대한수학회논문집2007 · 제22권 제1호Conditional generalized Fourier-Feynman transform of functionals in a Fresnel type class장승준대한수학회 · 대한수학회논문집2011 · 제26권 제2호A translation theorem for the generalized Fourier--Feynman transform associated with Gaussian process on function space장승준, 최재길, Ae Young Ko대한수학회 · 대한수학회지2016 · 제53권 제5호Change of scale formulas for function space integrals related with Fourier-Feynman transform and convolution on $C_{a,b}[0,T]$유일, 김병수, 김봉진강원경기수학회 · 한국수학논문집2015 · 제23권 제1호

이 간행물의 다른 논문 (9건)

Stability in nonlinear neutral Levin-Nohel integro-differential equationsAbdelouaheb Ardjouni, Kamel Ali Khelil, Ahcene Djoudipp. 303-321The reliable modified of Laplace adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equationsKIRTIWANT P. GHADLE, Ahmed A. Hamoudpp. 323-334Constructive proof for the positivity of the orbit polynomial $O_d^{n,2}(q)$이재진pp. 349-358Solvability for a system of generalized nonlinear ordered variational inclusions in ordered Banach spacesSalahuddinpp. 359-377Self-dual codes over ${\mathbb Z}_{p^2}$ of small lengths최환혁, 박영호pp. 379-388
원문 보기