Abstract
It is shown that a selfadjoint operator defined by a Dirichlet form perturbed by a measure can be described as a suitable maximal operator, for a wide class of measures. The generalized ‘distributional notion’ employed in the description reduces to the usual one for the case of Schrödinger operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albeverio, S. and Ma, Z.: 'Additive functionals, nowhere Radon and Kato class smooth measures associated with Dirichlet forms', Osaka J. Math. 29 (1992), 247–265.
Brézis, H. and Browder, F. E.: 'Sur une propriété des espaces de Sobolev', C.R. Acad. Sci. Paris Ser. A 287 (1978), 113–115.
Brézis, H. and Kato, T.: 'Remarks on the Schrödinger operator with singular complex potentials', J. Math. Pures Appl. 58 (1979), 137–151.
Bouleau, N. and Hirsch, F.: Dirichlet Forms and Analysis on Wiener Space, de Gruyter, Berlin, 1991.
Fukushima, M., Oshima, Y., and Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994.
Kato, T.: Perturbation Theory for Linear Operators, 2nd edn, Springer, New York, 1980.
Kato, T.: 'A second look at the essential self-adjointness of Schrödinger operators', in C. P. Enz and J. Mehra (eds.), Physical Reality and Mathematical Description, Reidel, Dordrecht, 1974.
Ma, Z.-M. and Röckner, M.: Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer, Berlin, 1992.
Reed, M. and Simon, B.: Methods of Modern Mathematical Physics. I: Functional Analysis, Academic Press, New York, 1980.
Reed, M. and Simon, B.: Methods of Modern Mathematical Physics. IV: Analysis of Operators, Academic Press, New York, 1978.
Stollmann, P.: 'Smooth perturbations of regular Dirichlet forms', Proc. Amer. Math. Soc. 116 (1992), 747–752.
Stollmann, P. and Voigt, J.: 'A regular potential which is nowhere in L1', Lett. Math. Phys. 9 (1985), 227–230.
Stollmann, P. and Voigt, J.: 'Perturbations of Dirichlet forms by measures', Potential Anal. 5 (1996), 109–138.
Voigt, J.: 'Absorption semigroups, their generators, and Schrödinger semigroups', J. Funct. Anal. 67 (1986), 167–205.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Manavi, A., Voigt, J. Maximal Operators Associated with Dirichlet Forms Perturbed by Measures. Potential Analysis 16, 341–346 (2002). https://doi.org/10.1023/A:1014839528598
Issue Date:
DOI: https://doi.org/10.1023/A:1014839528598