Korean J. Math. Vol. 32 No. 4 (2024) pp.769-782
DOI: https://doi.org/10.11568/kjm.2024.32.4.769

Existence theorems and evaluation formulas for sequential Yeh-Feynman integrals

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Published: Dec 30, 2024
Keywords:
Yeh-Wiener space, sequential Feynman integral, sequential Yeh-Feynman integral, Banach algebra $\hat{\mathcal S}(L_2(Q))$
Mathematics Subject Classification:
28C20, 46G12

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Byoung Soo Kim
School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Korea
Young-Hee Kim
Ingenium College of Liberal Arts, Kwangwoon University Seoul 01897, Korea

Abstract

We establish the existence of the sequential Yeh-Feynman integral for functionals of the form $F(x)=G(x)\Psi(x(S,T))$, where $G$ belongs to a Banach algebra of sequential Yeh-Feynman integrable functionals and $\Psi$ need not be bounded or continuous. We also give formulas evaluating the integrals of these functionals. Note that these functionals are often employed in the application of the Feynman integral to quantum theory, and $\Psi$ corresponds to the initial condition associated with Schr\"odinger equation.



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This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

Supporting Agencies

This study was supported by the Research Program funded by the SeoulTech(Seoul National University of Science and Technology).

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