Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and ConvolutionReport as inadecuate




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Journal of Function SpacesVolume 2014 2014, Article ID 657934, 7 pages

Research Article

Department of Mathematics, Daejin University, Pocheon 487-711, Republic of Korea

School of Liberal Arts, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea

Department of Mathematics, Yonsei University, Wonju 220-710, Republic of Korea

Received 18 April 2014; Accepted 19 May 2014; Published 26 June 2014

Academic Editor: Ismat Beg

Copyright © 2014 Bong Jin Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class and in a generalized Fresnel class on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.





Author: Bong Jin Kim, Byoung Soo Kim, and Il Yoo

Source: https://www.hindawi.com/



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