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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.9
- 수록면
- 1,035 - 1,050 (16page)
- DOI
- 10.4134/JKMS.j230437
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초록· 키워드
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The Cameron--Martin translation theorem describes how \linebreak Wiener measure changes under translation by elements of the Cameron--Martin space in an abstract Wiener space (AWS). Translation theorems for the analytic Feynman integrals also have been established in the literature. In this article, we derive a more general translation theorem for the analytic Feynman integral associated with bounded linear operators (B.L.OP.) on AWSs. To do this, we use a certain behavior which exists between the analytic Fourier--Feynman transform (FFT) and the convolution product (CP) of functionals on AWS. As an interesting application, we apply this translation theorem to evaluate the analytic Feynman integral of the functional \[ F(x)=\exp\bigg(-iq \int_0^Tx(t)y(t)d t \bigg),\quad y\in C_0[0,T], \, q\in\mathbb R\setminus\{0\} \] defined on the classical Wiener space $C_0[0,T]$.
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