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Semiclassical asymptotics of the spectral function of the magnetic Schrodinger operator

Yu. A. Kordyukov

Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa



Аннотация: In the talk, we discuss asymptotic spectral properties of the Schrodinger operator with uniformly bounded magnetic field in Euclidean space in the semiclassical limit. We give a rough asymptotic description of its spectrum and describe the full off-diagonal asymptotic expansion of its smoothed spectral function. As consequences, we obtain the semiclassical trace formula and an asymptotic localization property of the spectral function in the case when the magnetic field has maximal rank.

Язык доклада: английский


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