Structure of spectrum of Schrödinger operator with quasiperiodic potential near the ground state. The discrete and continuous cases

For a quasiperiodic Schrödinger operator whose ground state possesses certain properties, the structure of the spectrum near its left edge is investigated. An estimate is obtained for the measure of the excluded zones as a function of the rate of approximation of the rotation number by rational numbers. Both discrete and continuous operators are considered.