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A note on regular Dirichlet subspaces

Author(s): Masatoshi Fukushima; Jiangang Ying
Journal: Proc. Amer. Math. Soc. 131 (2003), 1607-1610.
MSC (1991): Primary 60J45, 60J65, 31B15
Posted: September 19, 2002
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Abstract: In this short article we shall consider the Dirichlet space associated with the distorted Brownian motion on a one-dimensional closed interval and prove that it admits no proper regular Dirichlet subspaces.

References:

1.: Fukushima, M., Oshima, Y., Takeda, M., Dirichlet forms and symmetric Markov processes, Walter de Gruyter, Berlin-New York, 1994. MR 96f:60126
2.: Rudin, W., Real and complex analysis, McGraw-Hill, 1986. MR 88k:00002
3.: Ying, J., Killing and subordination, Proc. Amer. Math. Soc. 124, No. 7(1996), pp. 2215-2222. MR 97a:31005
4.: Yoshida, K., Functional analysis, Springer-Verlag, 1965

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Additional Information:

Masatoshi Fukushima
Affiliation: Department of Mathematics, Kansai University, Osaka 564-8680, Japan
Email: fuku@ipcku.kansai-u.ac.jp

Jiangang Ying
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China
Email: jying@math.zju.edu.cn

DOI: 10.1090/S0002-9939-02-06656-X
PII: S 0002-9939(02)06656-X
Keywords: Regular Dirichlet space, distorted Brownian motion
Received by editor(s): August 3, 2001
Received by editor(s) in revised form: December 18, 2001
Posted: September 19, 2002
Additional Notes: The research of the first author was supported in part by Grant-in-Aid for Scientific Research (C) (2)
The research of the second author was supported in part by NNSF of China 19501036
Communicated by: Claudia M. Neuhauser
Copyright of article: Copyright 2002, American Mathematical Society


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