Generalized Fourier–Feynman transforms and generalized convolution products on Wiener space II

被引：0
作者：
Sang Kil Shim
Jae Gil Choi
机构：
[1] Dankook University,Department of Mathematics
[2] Dankook University,School of General Education
来源：
Annals of Functional Analysis | 2020年 / 11卷
关键词：
Wiener space; Gaussian process; Generalized Fourier–Feynman transform; Generalized convolution product; 46G12; 28C20; 60G15; 60J65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The purpose of this article is to present the second type fundamental relationship between the generalized Fourier–Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions (to the case on an infinite dimensional Banach space) of the structure which exists between the Fourier transform and the convolution of functions on Euclidean spaces.
引用
收藏
页码：439 / 457
页数：18
相关论文
共 36 条
  • [1] Chang KS(2005)Relationships involving generalized Fourier–Feynman transform, convolution and first variation Integral Transforms Spec. Funct. 16 391-405
  • [2] Cho DH(2017)Generalized Fourier–Feynman transforms and generalized convolution products on Wiener space Indag. Math. 28 566-579
  • [3] Kim BS(1993)Generalized Feynman integrals via conditional Feynman integrals Mich. Math. J. 40 377-391
  • [4] Song TS(1995)Analytic Fourier–Feynman transforms and convolution Trans. Am. Math. Soc. 347 661-673
  • [5] Yoo I(1996)Convolutions and Fourier–Feynman transforms of functionals involving multiple integrals Mich. Math. J. 43 247-261
  • [6] Chang SJ(1997)Convolution and Fourier–Feynman transforms Rocky Mt. J. Math. 27 827-841
  • [7] Chung HS(1997)Generalized transforms and convolutions Int. J. Math. Math. Sci. 20 19-32
  • [8] Choi JG(1933)Notes on random functions Math. Z. 37 647-668
  • [9] Chung DM(1969)A generalized Paley–Wiener–Zygmund integral and its applications Proc. Am. Math. Soc. 23 388-400
  • [10] Park C(1988)A note on Paley–Wiener–Zygmund stochastic integrals Proc. Am. Math. Soc. 103 591-601
1234