Browse > Article
http://dx.doi.org/10.14317/jami.2013.825

YEH CONVOLUTION OF WHITE NOISE FUNCTIONALS  

Ji, Un Cig (Department of Mathematics, Research institute of Mathematical Finance, Chungbuk National University)
Kim, Young Yi (Research institute for Natural Science, Hanyang University)
Park, Yoon Jung (Department of Mathematics, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 825-834 More about this Journal
Abstract
In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.
Keywords
white noise theory; Yeh convolution; Fourier-Gauss transform; Fourier-Mehler transform;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 D.M. Chung, T.S. Chung and U.C. Ji, A simple proof of analytic characterization theorem for operator symbols, Bull. Korean Math. Soc. 34 (1997), 421-436.   과학기술학회마을
2 D.M. Chung and U.C. Ji, Transforms groups on white noise functionals and their appli-cations, Appl. Math. Optim. 37 (1998), 205-223.
3 L. Gross, Potential theory on Hilbert space, J. Funct. Anal. 1 (1967), 123-181.   DOI
4 T. Hida, Analysis of Brownian Functionals, Carleton Math. Lect. Notes 3, 241-272.
5 M.K. Im, U.C. Ji and Y.J. Park, Relations between the first variation, the convolutions and the generalized Fourier-Gauss transforms, Bull. Korean Math. Soc. 48 (2011), 291-302.   DOI   ScienceOn
6 H.-H. Kuo, J. Potthoff and L. Streit, A characterization of white noise test functionals, Nagoya Math. J. 121 (1991), 185-194.   DOI
7 U.C. Ji and Y.Y. Kim, Convolution of white noise operators, Bull. Korean Math. Soc. 48 (2011), 1003-1014.   DOI   ScienceOn
8 U.C. Ji and N. Obata, A unified characterization theorem in white noise theory, Infin. Dim. Anal. Quantum Probab. Related Topics 6 (2003), 167-178.   DOI   ScienceOn
9 H.-H. Kuo, White Noise Distribution Theory, CRC Press, 1996.
10 Y.J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), 153-164.   DOI
11 N. Obata, An analytic characterization of symbols of operators on white noise functionals, J. Math. Soc. Japan 45 (1993), 421-445.   DOI
12 N. Obata, White Noise Calculus and Fock Space, Lect. Notes on Math. 1577, Springer-Verlag, Berlin, 1994.
13 J. Potthoff and L. Streit, A characterization of Hida distributions, J. Funct. Anal. 101 (1991), 212-229.   DOI
14 J. Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738.   DOI