Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum
Abstract
We study the 1-D Schr\"odinger operators in Hilbert space L2(R) with real-valued Radon measure q'(x), q∈ BVloc(R) as potentials. New sufficient conditions for minimal operators to be bounded below and selfadjoint are found. For such operators a criterion for the discreteness of the spectrum is proved, which generalizes Molchanov's, Brinck's, and the Albeverio-Kostenko-Malamud criteria. The quadratic forms corresponding to the investigated operators are described.
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