25
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

A (Co)-group generated by the lévy laplacian

Pages 567-584 | Published online: 03 Apr 2007

References

  • Feller , M.N. 1986 . Infinite-dimensional elliptic equations and operators of Lévy type . Russian Math. Surveys , 41 ( 4 ) : 119 – 170 .
  • Gross , L. . Abstract Wiener spaces . Proc. 5th Berkeley Symp. Math. Stat. Probab . Vol. 2 , pp. 31 – 42 . Berkeley : Univ. Berkeley .
  • Gross , L. 1967 . Potential theory on Hilbert space . J. Fund. Anal , 1 : 123 – 181 .
  • Hida , T. 1975 . “ Analysis of Brownian Functionals ” . In Carleton Math , Ottawa : Carleton University . Lecture Notes, No. 13
  • Hida , T. 1980 . “ Brownian motion ” . In Application of Math , Vol. 11 , Springer-Verlag .
  • Hida , T. 1992 . “ 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 , Springer-Verlag .
  • Hida , T. . Random Fields as Generalized White Noise Functionals . Proc. IFIP Enschede .
  • Hida , T. , Kuo , H.H. and Obata , N. 1990 . Transformations for white noise functionals . J. Fund. Anal , 111 : 259 – 277 .
  • Hida , T. , Kuo , H.H. , Potthoff , J. and Streit , L. 1993 . White Noise: An Infinite Dimensional Calculus , Kluwer Academic .
  • Hida , T. and Saitô , K. 1988 . “ White noise analysis and the Lévy Laplacian ” . In Stochastic Processes in Physics and Engineering 177 – 184 .
  • Hida , T. , Obata , N. and Saitô , K. 1992 . Infinite dimensional rotations and Laplacian in terms of white noise calculus . Nagoya Math. J , 128 : 65 – 93 .
  • Itô , K. . Stochastic analysis in infinite dimensions . Proc. International conference on stochastic analysis . pp. 187 – 197 . Evanston : Academic Press .
  • Kubo I. Takenaka S. Calculus on Gaussian white noise I, II, III and IV Proc. Japan Acad. 56 A (1980) 376-380; 56A (1980) 411- 416; 57A (1981) 433-436; 58A (1982) 186-189
  • Kuo , H.H. 1975 . “ Gaussian measures in Banach spaces ” . In Lecture Notes in Math , Vol. 463 , Springer-Verlag .
  • Kuo , H.H. . Fourier-Mehler transforms of generalized Brownian functionals . Proc. Japan. Acad . Vol. 59A , pp. 312 – 314 .
  • Kuo , H.H. 1986 . “ On Laplacian operators of generalized Brownian functionals ” . In Lecture Notes in Math , Vol. 1203 , Springer-Verlag .
  • Kuo , H.H. 1989 . The Fourier transform in white noise calculus . J. Multi. Anal , 31 : 311 – 327 .
  • Kuo , H.H. . Fourier-Mehler Transforms in white noise analysis . Gaussian Random Fields, the Third Nagoya Lévy Seminar . Edited by: Itô , K. and Hida , T. pp. 257 – 271 . World Scientific
  • Kuo , H.H. 1992 . “ Convolution and Fourier transform of Hida distributions ” . In Lecture Notes in Control and Information Sciences , Vol. 176 , 165 – 176 . Springer-Verlag .
  • Kuo , H.H. 1992 . An infinite dimensional Fourier transform . Aportaciones Matemáticas Notas de Investigatión , 7 : 1 – 12 .
  • Kou , H.H. 1996 . White Noise Distribution Theory , CRC Press .
  • Kuo , H.H. , Obata , N. and Saitô , K. 1990 . Lévy Laplacian of generalized functions on a nuclear space . J. Funct. Anal , 94 : 74 – 92 .
  • Lévy , P. 1922 . Lecons d’analyse fonctionnelle , Paris : Gauthier-Villars .
  • Lévy , P. 1951 . Problèmes concrets d’analyse fonctionnelle , Paris : Gauthier-Villars .
  • Obata , N. 1990 . A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups . Nagoya Math. J , 118 : 111 – 132 .
  • Obata , N. 1994 . “ White Noise Calculus and Fock Space ” . In Lecture Notes in Mathematics , Vol. 1577 , Springer-Verlag .
  • Polishchuck , E.M. 1988 . Continual Means and Boundary Value Problem in Function Spaces , Birkhäuther .
  • Potthoff , J. and Streit , L. 1991 . A characterization of Hida distributions . J. Funct. Anal , 101 : 212 – 229 .
  • Saitô , K. 1987 . Itô's formula and Lévy's Laplacian I and II . Nagoya Math. J , 108 : 67 – 76 . 123 (1991), 153-169
  • Saitô , K. . On a construction of a space of generalized functionals . Proc. Preseminar for Int. Conf. on Gaussian Random Fields . Vol. 2 , pp. 20 – 26 . Part
  • Saitô K. The Lévy Laplacian in white noise analysis Preprint 1992
  • Yosida , K. 1971 . Functional Analysis , Springer-Verlag .
  • Zhang , Y. 1995 . The Lévy Laplacian and Brownian particles in Hilbert spaces . J. Funct Anal , 133 : 425 – 441 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.