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Showing 2008 · math.SPShow all
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math.SP2008
Bethe-Sommerfeld conjecture for pseudodifferential perturbation
G. Barbatis, L. Parnovski
We consider a periodic pseudodifferential operator () in which satisfies the following conditions: (i) the symbol of is smooth in , and (ii) the per…
math.SP2008★ 54 cited
Bethe-Sommerfeld Conjecture
Leonid Parnovski
We consider Schroedinger operator in () with smooth periodic potential and prove that there are only finitely many gaps in its spectrum.
math.SP2008★ 1 cited
Fourier transform, null variety, and Laplacian's eigenvalues
Rafael Benguria, Michael Levitin, Leonid Parnovski
We consider a quantity -- the distance to the origin from the null variety of the Fourier transform of the characteristic function of . We conjecture, firstly, that $κ(Ω)…