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2010 | 8 | 5 | 908-927
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Operator-valued Feynman integral via conditional Feynman integrals on a function space

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EN
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 $$ \Gamma _t \left( x \right) = exp \left\{ {\int_0^t {\theta \left( {s,x\left( s \right)} \right)d\eta \left( s \right)} } \right\}\varphi \left( {x\left( t \right)} \right) x \in C^r \left[ {0,t} \right] $$, 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 an integral transform as an analytic operator-valued Feynman integral over C r [0, t], and evaluate the integral transform for the function Γt via the conditional analytic Feynman integral as a kernel.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
5
Strony
908-927
Opis fizyczny
Daty
wydano
2010-10-01
online
2010-09-28
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autor
Bibliografia
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-010-0059-7
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