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Invariance of essential spectra for generalized Schrödinger operators. (English) Zbl 1136.35339

Summary: We give a new sufficient condition for the invariance of the essential spectrum of \(-\Delta+\mu\), where \(\mu\) is a signed Radon measure. This condition is formulated in term of the behavior of the ratio of the \(|\mu|\)-measure of compact subsets by their \(2\)-order capacity at infinity. Our method recovers a large class of measures.

MSC:

35J10 Schrödinger operator, Schrödinger equation
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
35P05 General topics in linear spectral theory for PDEs
47F05 General theory of partial differential operators
47N50 Applications of operator theory in the physical sciences
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