Displaying similar documents to “A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space.”

Operator-valued Feynman integral via conditional Feynman integrals on a function space

Dong Cho (2010)

Open Mathematics

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Let C 0r [0; t] denote the analogue of the r-dimensional Wiener space, define X t: C r[0; t] → ℝ2r by X t (x) = (x(0); x(t)). In this paper, we introduce a simple formula for the conditional expectations with the conditioning function X t. Using this formula, we evaluate the conditional analytic Feynman integral for the functional Γ t x = e x p ∫ 0 t θ s , x s d η s ϕ x t x ∈ C r 0 , t , where η is a complex Borel measure on [0, t], and θ(s, ·) and φ are the Fourier-Stieltjes transforms of the complex Borel measures on ℝr. We then introduce...

A failure of quantifier elimination.

Angus Macintyre, David Marker (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.

Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim, Il Yoo, Dong Cho (2010)

Open Mathematics

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Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class ℱ 𝒜 1 , 𝒜 2 A1,A2 than the Fresnel class ℱ (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space...