On the Uniqueness Problem for Dirichlet Operators

Journal of Functional Analysis

Volumn 162, Issue 1, 1999, Pages 1-13

  Liskevich, Vitali ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011381031     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3365     Document Type: Article

References (19)

1. Albeverio S., Hoegh-Krohn R., Streit L. Energy forms, Hamiltonians and distorted Brownian paths. J. Math. Phys. 18:1977;907-917.
2. Berezanskii Yu. M., Kondratiev Yu. G. Spectral Methods in Infinite Dimensional Analysis. 1988;Naukova Dumka, Kiev.
3. n. Ann. Scuola Norm Sup. Pisa. 24:1997;451-462.
4. Cattiaux P., Fradon M. Entropy, reversible diffusion processes and Markov uniqueness. J. Funct. Anal. 138:1996;243-272.
5. 1. Bull. London Math. Soc. 17:1985;417-436.
6. Davies E. B. Heat kernel bounds, conservation of probability, and the Feller property. J. Analyse. 58:1992;99-119.
7. Davies E. B. Heat Kernels and Spectral Theory. 1989;Cambridge Univ. Press, Cambridge/New York.
8. Eberle A. Uniqueness and Non-uniqueness of Singular Diffusion Operators. 1997.
9. Fukushima M., Oshima Y., Takeda M. Dirichlet Forms and Symmetric Markov Processes. 1994;de Gruyter, Berlin/New York.
10. Liskevich V. A., Semenov Yu. A. Some problems on Markov semigroups. Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras. Mathematical Topics: Advances in Partial Differential Equations. 11:1996;Akademie Verlag, Berlin. p. 163-217.
11. Liskevich V. A. Smoothness estimates and uniqueness for the Dirichlet operator. Operator Theory: Advances and Applications. 1994;Birkhäuser, Basel. p. 149-152.
12. Liskevich V. A., Semenov Yu. A. Dirichlet operators: a-priori estimates and the uniqueness problem. J. Funct. Anal. 109:1992;199-213.
13. Perelmuter M. A., Semenov Yu. A. Elliptic operators preserving probability. Theory Probab. Appl. 32:1987;718-721.
14. Reed M., Simon B. Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-adjointness. 1975;Academic Press, New York/San Francisco/London.
15. Röckner M., Zhang T.-S. Uniqueness of generalized Schrödinger operators and applications. J. Funct. Anal. 119:1994;455-467.
16. 1.
17. Sturm K.-Th. Analysis on local Dirichlet spaces, I. J. Reine Angew. Math. 456:1996;173-196.
18. Taira K. On the existence of Feller semigroups with Dirichlet condition. Tsukuba J. Math. 17:1993;377-427.
19. Taira K. On the existence of Feller semigroups with boundary conditions, II. J. Funct. Anal. 129:1995;108-131.