Vladimir Buslaev, Alexander Fedotov
On the Point Spectrum of Diffirence Schrödinger operators
Preprint series: ESI preprints

MSC:

39A10 Difference equations, See also {33Dxx}

47B39 Difference operators, See also {39A70}

34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)

Abstract: One considers the equation
$\psi\,(x+h)+\psi\,(x-h)+v\,(x)\,\psi\,(x)=E\psi\,(x)$,
where $v$ is an almost everywhere finite periodic function, and $h$ is a
positive number. It is proved that this equation has no solutions from
$L_2(\Bbb R)$.
This implies in particular that the spectrum of Harper operator appears to be
singular continuous in all the cases where its geometrical structure
was investigated.

Keywords: Difference Schroedinger operator, Harper operator