The essential self-adjointness of generalized Schrödinger operators |
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Authors: | Norbert Wielens |
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Affiliation: | Fakultät für Mathematik, Universität Bielefeld, D-4800 Bielefeld 1, West Germany |
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Abstract: | A necessary and sufficient condition is given for the generalized Schrödinger operator to be essentially self-adjoint in , under general assumptions on ? and for arbitrary domains Ω in n. In particular, if ? is strictly positive and locally Lipschitz continuous on , then A is essentially. self-adjoint. Examples of non-essential self-adjointness and a complete discussion of the one-dimensional case are also given. These results have applications to the problem of the essential self-adjointness of quantum Hamiltonians and to the uniqueness problem of Markov processes. |
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