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In the following we consider a positive complete Borel measure on R to be a countably additive set function u from the Borel subsets BR to R+, with the additional property that all subsets of measure zero sets are measurable.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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total spectral measure, second resolvent equation, feller potential, cyclic family, sparse potentials, singular spectra, finite complex measure, absolutely continuous spectrum, selfadjoint operator, perturbed operators, random operators, singular continuous spectrum, selfadjoint extension, cyclic subspace, trace class operator, wave operators, singular with respect, spectral theorem, cyclic vector, resolvent kernels, admissible function, absolutely continuous part, trace norm, random potentials, pure point
Key Phrases - Capitalized Phrases (CAPs):
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Hilbert Schmidt, Reed Simon, Operators of Interest, Notes Section, Demuth van Casteren, Baumgärtel Wollenberg, Characterization of the States, Engel Nagel, Figotin Pastur, Gilbert Pearson, Pearson's Theorem
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