Korean J. Math.  Vol 27, No 2 (2019)  pp.445-463
DOI: https://doi.org/10.11568/kjm.2019.27.2.445

A Banach algebra of series of functions over paths

Dong Hyun Cho, Mo A Kwon

Abstract


Let $C[0,T]$ denote the space of continuous real-valued functions on $[0,T]$. On the space $C[0,T]$, we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.

Keywords


Analytic Wiener integral, analytic Feynman integral, Banach algebra, It\^o integral, Paley-Wiener-Zygmund integral, Wiener space

Subject classification

46J10, 28C20, 60H05.

Sponsor(s)

the National Research Foundation (NRF) of Korea

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References


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