On spectral properties of one-dimensional disperse crystals

The connection between spectral characteristics of one-dimensional Schrödinger operator $l_a(y)=-y''+q_a(x)y$ with a periodic potential $q_a=\sum_{n=-\infty}^\infty q(x-na)$ as $a\to\infty$ and spectral characteristics of the Schrödinger operator $l(y)=-y''+q(x)y$ with decreasing potential $q(x)$ is studed.