Proceedings of the American Mathematical Society

Author(s): Dong Myung Chung; Un Cig Ji; Kimiaki Saitô
Journal: Proc. Amer. Math. Soc. 130 (2002), 1197-1206.
MSC (2000): Primary 60H40
Posted: September 19, 2001
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Abstract: In this paper we shall give some results on a

-group generated by the Lévy Laplacian and operators approximating that group in the space $\mathcal{ L}({\mathbf E})$ of continuous linear operators defined on a certain locally convex space ${\mathbf E}$ in $(\mathcal{S})^*.$

1.: Accardi, L.: Yang-Mills equations and the Lévy Laplacian, in ``Dirichlet Forms and Stochastic Processes'', (Z.M. Ma, M. Röckner and J.A. Yan eds.) de Gruyter, 1-24, 1995. MR 97c:46093
2.: Chung, D. M. and Ji, U. C.: Transforms on white noise functionals with their applications to Cauchy problems, Nagoya Math J. 147 (1997), 1-23. MR 99b:60098
3.: Chung, D. M., Ji, U. C. and Saitô, K.: Cauchy problems associated with the Lévy Laplacian in white noise analysis, Infinite Dimensional Analysis, Quantum Probability and Related Topics 2, No.1 (1999), 131-153.
4.: Gross, L.: Abstract Wiener spaces; Proc. 5th Berkeley Symp. Math. Stat. Probab. 2 (1965), 31-42. Berkeley: Univ. Berkeley. MR 35:3027
5.: Gross, L.: Potential theory on Hilbert space; J. Func. Anal. 1 (1967), 123-181. MR 37:3331
6.: Hida, T.: ``Analysis of Brownian Functionals", Carleton Math. Lecture Notes, No.13, Carleton University, Ottawa, 1975. MR 56:9715
7.: Hida, T.: A role of the Lévy Laplacian in the causal calculus of generalized white noise functionals, in `` Stochastic Processes A Festschrift in Honour of G. Kallianpur '' (S. Cambanis et al. Eds.) Springer-Verlag, 1992. MR 97j:6049
8.: Hida, T., Kuo, H. - H. and Obata, N.: Transformations for white noise functionals, J. Funct. Anal. 111 (1990), 259-277. MR 93m:46042
9.: Hida, T., Kuo, H. - H., Potthoff, J. and Streit, L.: ``White Noise: An Infinite Dimensional Calculus", Kluwer Academic, 1993. MR 95f:60046
10.: Hida, T. and Saitô, K.: White noise analysis and the Lévy Laplacian, in ``Stochastic Processes in Physics and Engineering" (S. Albeverio et al. Eds.), 177-184, 1988. MR 89m:60092
11.: Hida, T., Obata, N. and Saitô, K.: Infinite dimensional rotations and Laplacian in terms of white noise calculus, Nagoya Math. J. 128 (1992), 65-93. MR 94a:60119
12.: Itô, K.: Stochastic analysis in infinite dimensions, in ``Proc. International conference on stochastic analysis'', Academic Press, Evanston, 187-197, 1978. MR 80k:60073
13.: Kubo, I.: A direct setting of white noise calculus, in: Stochastic analysis on infinite dimensional spaces, Pitman Research Notes in Mathematics Series, 310 (1994), 152-166. MR 98b:60072
14.: Kubo, I. and Takenaka, S.: Calculus on Gaussian white noise I, II, III and IV, Proc. Japan Acad. 56A (1980), 376-380; 56A (1980), 411-416; 57A (1981), 433-436; 58A (1982), 186-189. MR 84d:60062; MR 84d:60063a; MR 84d:60063b; MR 84m:60100
15.: Kuo, H. - H.: On Laplacian operators of generalized Brownian functionals, in ``Lecture Notes in Math.'' 1203, Springer-Verlag, 119-128, 1986. MR 88e:60078
16.: Kuo, H. - H.: White noise distribution theory, CRC Press (1996). MR 97m:60056
17.: Kuo, H. - H., Obata, N. and Saitô, K.: Lévy Laplacian of generalized functions on a nuclear space, J. Funct. Anal. 94 (1990), 74-92. MR 91m:46061
18.: Lee, Y.-J.: Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1983), 153-164. MR 84j:28021
19.: Lee, Y.-J.: Unitary operators on the space of -functions over abstract Wiener spaces, Soochow J. Math. 13 (1987), 165-174. MR 89h:47045
20.: Lévy, P.: ``Lecons d'analyse fonctionnelle", Gauthier-Villars, Paris, 1922.
21.: Obata, N.: A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups, Nagoya Math. J. 118 (1990), 111-132. MR 91m:46063
22.: Obata, N.: ``White Noise Calculus and Fock Space,'' Lecture Notes in Mathematics 1577, Springer-Verlag, 1994. MR 96e:60061
23.: Potthoff, J. and Streit, L.: A characterization of Hida distributions, J. Funct. Anal. 101 (1991), 212-229. MR 93a:46078
24.: Saitô, K.: Itô's formula and Lévy's Laplacian I and II, Nagoya Math. J. 108 (1987), 67-76; 123 (1991), 153-169. MR 89f:60042; MR 93c:60057
25.: Saitô, K.: A group generated by the Lévy Laplacian and the Fourier-Mehler transform, in: Stochastic analysis on infinite dimensional spaces, Pitman Research Notes in Mathematics Series 310 (1994), 274-288. MR 97i:60107
26.: Saitô, K.: A -group generated by the Lévy Laplacian, Journal of Stochastic Analysis and Applications 16, No. 3 (1998), 567-584. MR 99g:60109
27.: Saitô, K.: A -group generated by the Lévy Laplacian II, Infinite Dimensional Analysis, Quantum Probability and Related Topics 1, No. 3 (1998), 425-437. MR 99k:46074
28.: Yosida, K.: ``Functional Analysis 3rd Edition", Springer-Verlag, 1971. MR 39:741 (review of 2nd edition)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60H40

Dong Myung Chung
Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Email: dmchung@ccs.sogang.ac.kr

Un Cig Ji
Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Email: ucji@nuri.net

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