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A CAMERON-STORVICK THEOREM ON C2a,b[0, T ] WITH APPLICATIONS

  • Choi, Jae Gil (School of General Education Dankook University) ;
  • Skoug, David (Department of Mathematics University of Nebraska-Lincoln)
  • Received : 2020.08.10
  • Accepted : 2021.01.20
  • Published : 2021.10.31
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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 C2a,b[0, T]. The function space Ca,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 ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C2a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C2a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

Keywords

Acknowledgement

The authors would like to express their gratitude to the editor and the referees for their valuable comments and suggestions which have improved the original paper.

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