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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2021.10
- 수록면
- 685 - 704 (20page)
- DOI
- 10.4134/CKMS.c200297
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초록· 키워드
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The purpose of this paper is to establish a very general Cameron--Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space $C_{a,b}^2[0,T]$. The function space $C_{a,b}[0,T]$ can be induced by the generalized Brownian motion process associated with continuous functions $a$ and $b$. To do this we first introduce the class $\mathcal F_{A_1,A_2}^{\,\,a,b}$ of functionals on $C_{a,b}^2[0,T]$ which is a generalization of the Kallianpur and Bromley Fresnel class $\mathcal F_{A_1,A_2}$. We then proceed to establish a Cameron--Storvick theorem on the product function space $C_{a,b}^2[0,T]$. Finally we use our Cameron--Storvick theorem to obtain several meaningful results and examples.
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참고문헌 (28)
참고문헌 신청
Robert H. Cameron / 1951 / The First Variation of an Indefinite Wiener Integral / Proceedings of the American Mathematical Society 2(6):914~924
R. H. Cameron / 1991 / Gaussian random fields / World Sci. Publ :144~157
S. J. Chang / 2016 / Effect of drift of the generalized Brownian motion process:an example for the analytic Feynman integral / Arch. Math. 106(6):591~600
S. J. Chang / 2015 / Multiple generalized analytic Fourier-Feynman transform via rotation of Gaussian paths on function space / Banach J. Math. Anal 9(4):58~80
Seung Chang / 2003 / Integration by parts formulas involving generalized Fourier-Feynman transforms on function space / Transactions of the American Mathematical Society 355(7):2925~2948
R. H. Cameron / 1991 / Gaussian random fields / World Sci. Publ :144~157
S. J. Chang / 2016 / Effect of drift of the generalized Brownian motion process:an example for the analytic Feynman integral / Arch. Math. 106(6):591~600
S. J. Chang / 2015 / Multiple generalized analytic Fourier-Feynman transform via rotation of Gaussian paths on function space / Banach J. Math. Anal 9(4):58~80
Seung Chang / 2003 / Integration by parts formulas involving generalized Fourier-Feynman transforms on function space / Transactions of the American Mathematical Society 355(7):2925~2948
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