Browse > Article

INFINITESIMAL GENERATORS OF THE GENERALIZED FOURIER-GAUSS TRANSFORMS  

Ji, Un Cig (Department of Mathematics Research Institute of Mathematical Finance Chungbuk National University)
Kim, Young Yi (Department of Mathematics Chungbuk National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.1, 2010 , pp. 1-10 More about this Journal
Abstract
In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.
Keywords
white noise theory; Gross Laplacian; number operator; Fourier-Gauss transform; Fourier-Mehler transform; infinitesimal generator;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. M. Chung and U. C. Ji, Transforms on white noise functionals with their applications to Cauchy problems, Nagoya Math. J. 147 (1997), 1-23.   DOI
2 D. M. Chung and U. C. Ji, Transformation groups on white noise functionals and their applications, Appl. Math. Optim. 37 (1998), 205-223.   DOI   ScienceOn
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 no. 13, Carleton University, Ottawa 1975.
5 T. Hida, H.-H. Kuo and N. Obata, Transformations for white noise functionals, J. Funct. Anal. 111 (1993), 259-277.   DOI   ScienceOn
6 U. C. Ji and N. Obata, Unitarity of generalized Fourier-Gauss transform, Stochastic Anal. Appl. 24 (2006), 733-751.   DOI   ScienceOn
7 U. C. Ji and N. Obata, Bogoliubov transformations in terms of generalized Fourier-Gauss transforms, Preprint, 2008.
8 H.-H. Kuo, White Noise Distribution Theory, CRC Press, 1996.
9 Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), 153-164.   DOI
10 N. Obata, An analytic characterization of symbols of operators on white noise functionals, J. Math. Soc. Japan 45 (1993), 421-445.   DOI
11 N. Obata, White Noise Calculus and Fock Space, Lect. Notes in Math. Vol. 1577, Springer-Verlag, 1994.