Analytic criteria in the qualitative spectral analysis of the Schroedinger operator

Details Analytic criteria in the qualitative spectral analysis of the Schroedinger operator Analytic criteria in the qualitative spectral analysis of the Schroedinger operator

2007-02-14

arxiv.org/abs/math/0702427v1

Mathematics

Spectral Theory

Scientific paper

A number of topics in the qualitative spectral analysis of the Schr\"odinger operator $-\Delta + V$ are surveyed. In particular, some old and new results concerning the positivity and semiboundedness of this operator as well as the structure of different parts of its spectrum are considered. The attention is focused on conditions both necessary and sufficient, as well as on their sharp corollaries.

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