Abstract
The Doss trick is employed to find solutions of Schrüdinger equations on symmetric spaces of compact type. The potentials and initial conditions are taken from an algebra of functions which admit an holomorphic extension to the complexification of the considered symmetric spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Albeverio Z. Brzeźniak Z. Haba (1998) ArticleTitleOn the Schrüdinger equations with potentials which are Laplace transforms of measures Pot. Anal. 9 65–82 Occurrence Handle10.1023/A:1008645118011
S. Albeverio A. Kherennikov O. Smolyanov (1999) ArticleTitleThe probabilistic Feynman–Kac formula for an infinite-dimensional Schrüdinger equation with exponential and singular potentials Pot. Anal. 11 157–181 Occurrence Handle10.1023/A:1008601707361
C.A. Berenstein R. Gay (1991) Complex Variables Springer-Verlag New York
Th. Brücker T. Tom Dieck (1985) Representation of Compact Lie Groups Springer-Verlag New York
H. Doss (1980) ArticleTitleSur une resolution stochastique de l’ equation de Schrüdinger à coefficients analytiques Comm. Math. Phys. 73 247–264 Occurrence Handle10.1007/BF01197701
H. Doss (1982) ArticleTitleDémonstration probabiliste de certains développments asymptotiques quasi classiques Bull. Sci. Math. 109 179–208
R.C. Gunning H. Rossi (1965) Analytic Functions of Several Complex Variables Prentice Hall Inc. Englewood Cliffs, N.J
B.C. Hall (1994) ArticleTitleThe Segal–Bargmann “Coherent state transform” for compact Lie groups J. Funct. Anal. 122 103–151 Occurrence Handle10.1006/jfan.1994.1064
S. Helgason (1978) Differential Geometry, Lie Groups and Symmetric Spaces, Pure and Applied Mathematics, 80 Academic Press New York
E. Hewitt K.A. Ross (1970) Abstract Harmonic Analysis II Springer-Verlag Berlin
J. Hilgert K.H. Neeb (1991) Lie-Gruppen und Lie-Algebren Vieweg Braunschweig
G. Hochschild (1965) The Structure of Lie Groups Holden-Day San Francisco
N. Ikeda Sh. Watanabe (1989) Stochastic Differential Equations and Diffusion Processes North-Holland Publishing Co. Amsterdam
Sh. Kobayashi K. Nomizu (1969) Foundations of Differential Geometry, Vol. II Interscience Publishers, John Wiley & Sons New York
E. Nelson (1959) ArticleTitleAnalytic vectors Ann. Math. 70 572–615
D.W. Robinson (1991) Elliptic Operators and Lie groups Clarendon press Oxford
H. Thaler (2003) ArticleTitleSolutions of Schrüdinger equations on compact Lie groups via probabilistic methods Pot. Anal. 18 119–140 Occurrence Handle10.1023/A:1020548720016
V.S. Varadarajan (1984) Lie Groups, Lie Algebras and their Representations Springer-Verlag New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Thaler, H. The Doss Trick on Symmetric Spaces. Lett Math Phys 72, 115–127 (2005). https://doi.org/10.1007/s11005-005-4395-7
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11005-005-4395-7