Korean J. Math. Vol. 23 No. 1 (2015) pp.47-64
DOI: https://doi.org/10.11568/kjm.2015.23.1.47

Change of scale formulas for function space integrals related with Fourier-Feynman transform and convolution on $C_{a,b}[0,T]$

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Published: Mar 30, 2015
Keywords:
change of scale formula, function space integral, generalized analytic Feynman integral, generalized Fourier-Feynman transform, convolution
Mathematics Subject Classification:
28C20, 60J25, 60J65

Main Article Content

Bong Jin Kim
Department of Mathematics Daejin University Pocheon 487-711, Korea
Byoung Soo Kim
School of Liberal Arts Seoul National University of Science and Technology Seoul 139-743, Korea
Il Yoo
Department of Mathematics Yonsei University Wonju 220-710, Korea

Abstract

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra ${\mathcal S}(L_{a,b}^2[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.


Article Details

Supporting Agencies

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

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