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Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

100%

Kim B., Yoo I., Cho D.

Open Mathematics

2010

tom 8

nr 3

616-632

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 $$ \mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 } $$ A1,A2 than the Fresnel class $$ \mathcal{F} $$(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 having the form $$ F\left( x \right) = G\left( x \right)\psi \left( {\left( {\vec e,x} \right)^ \sim } \right) $$, where G∈$$ \mathcal{F} $$(B)and Ψ = ψ + ϕ with ψ ∈ L 1(ℝn) and ϕ is the Fourier transform of a complex Borel measure of bounded variation on ℝn. We also prove a translation theorem for the analytic Feynman integral of the above functionals.

Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space

84%

Kim M.

Open Mathematics

2005

tom 3

nr 3

475-495

In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.

Ograniczanie wyników

2 Open Mathematics

1 Cho D.

1 Kim B.

1 Kim M.

1 Yoo I.

1 2010

1 2005

Wyniki wyszukiwania

Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space