Generalized analytic Feynman integral via function space integral of bounded cylinder functionals
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 475-489
Published online May 1, 2011
Seung Jun Chang, Jae Gil Choi, and Hyun Soo Chung
Dankook University, Dankook University, Dankook University
Abstract : In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form $$ F(x)=\hat\nu(( g_1, x)^{\sim}, \ldots, (g_n, x)^{\sim}) $$ defined on a very general function space $C_{a,b}[0,T]$. We also present a change of scale formula for function space integrals of such cylinder functionals.
Keywords : generalized Brownian motion, generalized analytic Feynman integral, function space integral, cylinder functional, change of scale formula
MSC numbers : 60J65, 28C20
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