The concept of complex Dirichlet forms epsilon_c resp.operators L_c in complex weighted L^2-spaces is introduced. Perturbations of classical Dirichlet forms by forms associated with complex first-order differential operators provide examples of complex Dirichlet forms. Complex Dirichlet operators L_c are unitarily equivalent with (a family of) Schroedinger operators with electromagnetic potentials. To epsilon_c there is associated a pair of real-valued non symmetric Dirichlet forms on the corresponding real weighted L^2-spaces, which in turn are associated with (non-symmetric) diffusion processes. Results by Stannat on non symmetric Dirichlet forms and their perturbations can be used for discussing the essential self-adjointness of L_c. New closability criteria for (perturbation of) non symmetric Dirichlet forms are obtained.

Complex Dirichlet Forms: Non symmetric Diffusion Processes and Schoedinger Operators / S. Albeverio, S. Ugolini. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 12:4(2000), pp. 403-417.

Complex Dirichlet Forms: Non symmetric Diffusion Processes and Schoedinger Operators

S. Ugolini
Ultimo
2000

Abstract

The concept of complex Dirichlet forms epsilon_c resp.operators L_c in complex weighted L^2-spaces is introduced. Perturbations of classical Dirichlet forms by forms associated with complex first-order differential operators provide examples of complex Dirichlet forms. Complex Dirichlet operators L_c are unitarily equivalent with (a family of) Schroedinger operators with electromagnetic potentials. To epsilon_c there is associated a pair of real-valued non symmetric Dirichlet forms on the corresponding real weighted L^2-spaces, which in turn are associated with (non-symmetric) diffusion processes. Results by Stannat on non symmetric Dirichlet forms and their perturbations can be used for discussing the essential self-adjointness of L_c. New closability criteria for (perturbation of) non symmetric Dirichlet forms are obtained.
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/164818
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