On the Polyharmonic Operator with a Periodic Potential

Details On the Polyharmonic Operator with a Periodic Potential On the Polyharmonic Operator with a Periodic Potential

2005-12-05

arxiv.org/abs/math-ph/0512008v1

Proceeding of the Institute Math. and Mech. of the Azerbaijan Acad. of Sciences no 2 (2005)

Physics

Mathematical Physics

Published in Proceeding of the Institute Math. and Mech. of the Azerbaijan Acad. of Sciences no 2 (2005)

Scientific paper

In this paper we obtain the asymptotic formulas of arbitrary order for the Bloch eigenvalues and Bloch functions of the multidimensional polyharmonic operator with periodic, with respect to arbitrary lattice, potential. Then we prove that the number of gaps in the spectrum of the operator is finite. In particular, we get the proof of the Bethe -Sommerfeld conjecture for arbitrary dimension and arbitrary lattice.

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