Spectral analysis of pseudodifferential operators |
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Authors: | R. A. Weder |
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Affiliation: | Katholieke Universiteit Leuven, Belgium |
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Abstract: | The subject of this paper is the spectral analysis of pseudodifferential operators in the framework of perturbation theory. We build up a closed extension (the closure, or the Friedrichs extension) of the perturbed operator. We also prove Weyl-type theorems on the invariance of the essential spectrum of the unperturbed operator. In the case when the perturbed operator is symmetric we obtain a self-adjoint extension. Finally, we consider the case of the relativistic, spin-zero Hamiltonian, with a large class of interactions containing both local potentials, like the Coulomb and Yukawa, and nonlocal ones. |
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