Atlas: $L_p$ Fourier-Feynman transform and the first variation on the Fresnel class by Jae Moon Ahn

Atlas home || Conferences | Abstracts | about Atlas

Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

View Abstracts
Conference Homepage

L_p Fourier-Feynman transform and the first variation on the Fresnel class
by
Jae Moon Ahn
Konkuk University (Republic of Korea)

Let F(B) be the Fresnel class on an abstract Wiener space (B, H, \omega) which consists of functionals F of the form :

F(x) = ó
õ

H
exp {i(h, x)^~ } df(h), x in B,

where (·, ·)^~ is a stochastic inner product between H and B , and f is in M(H), the space of all complex-valued countably additive Borel measures on H .

We introduce the concepts of an n-repeated L_p analytic Fourier- Feynman transform (1 <= p <= 2), a convolution product and the first variation for functionals in F(B) and verify the existence of the n-repeated L_p analytic Fourier-Feynman transforms for functionals in F(B). Moreover, we verify that the Fresnel class F(B) is closed under the L_p analytic Fourier-Feynman transformation and the convolution product, respectively. And we investigate some relationships among the n-repeated L_p analytic Fourier-Feynman transform, the convolution product and the first variation for functionals in F(B).

(T)

Date received: April 4, 2000