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In this article, we establish translation theorems for the analytic Fourier--Feynman transform of functionals in non-stationary Gaussian processes on Wiener space. We then proceed to show that these general translation theorems can be applied to two well-known classes of functionals; namely, the Banach algebra $\mathcal S$ introduced by Cameron and Storvick, and the space $\mathcal B_{\mathcal A}^{(p)}$ consisting of functionals of the form $F(x)=f(\langle{\alpha_1,x}\rangle,\ldots,\langle{\alpha_n,x}\rangle)$, where $\langle{\alpha,x}\rangle$ denotes the Paley--Wiener--Zygmund stochastic integral $\int_0^T \alpha(t)dx(t)$.
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참고문헌 (25)
참고문헌 신청
M. D. Brue / 1972 / A functional transform for Feynman integrals similar to the Fourier transform
R. H. Cameron / 1951 / Additive functionals on a space of continuous functions. I / Trans. Amer. Math. Soc. 70:160~176
R. H. Cameron / 1944 / Transformations of Wiener integrals under translations / Ann. of Math. 45:386~396
R. H. Cameron / 1966 / A translation theorem for analytic Feynman integrals / Trans. Math. Amer. Soc. 125:1~6
R. H. Cameron / 1976 / An $L_2$ analytic Fourier-Feynman transform / Michigan Math. J. 23(1):1~30
R. H. Cameron / 1951 / Additive functionals on a space of continuous functions. I / Trans. Amer. Math. Soc. 70:160~176
R. H. Cameron / 1944 / Transformations of Wiener integrals under translations / Ann. of Math. 45:386~396
R. H. Cameron / 1966 / A translation theorem for analytic Feynman integrals / Trans. Math. Amer. Soc. 125:1~6
R. H. Cameron / 1976 / An
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