Steklov Institute of Mathematics at St.Petersburg

PREPRINT 06/2004

ASYMPTOTIC BOUNDS FOR THE SPECTRAL BANDS OF PERIODIC SCHR\"ODINGER OPERATORS

This preprint was accepted June 6, 2004

ABSTRACT:
We obtain sharp upper and lower bounds for the overlap
multiplicity of spectral bands of the multidimensional
Schr\"odinger operator with a rational lattice of periods.
These bounds are based on recent results on the lattice
counting.