A Cameron-Storvick type theorem on C_a,b²[0,T] with applications

2020/01/15 by Jae Gil Choi, Choi, Jae Gil, David Skoug +1
Mathematics · #28C20 #46G12 #60J65 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Meromorphic and Entire Functions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2001.05595

openalex publication_date 2020/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C_a,b²[0,T]. The function space C_a,b[0,T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class \mathcal F_A1,A2 ^a,b of functionals on C_a,b²[0,T] which is a generalization of the Kallianpur and Bromley Fresnel class \mathcal F_A1,A2. We then proceed to establish a Cameron-Storvick type theorem on the product function space C_a,b²[0,T]. Finally we use our Cameron--Storvick type theorem to obtain several meaningful results and examples.

Citations

• Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral

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