Monodromization and the Harper equation. (English) Zbl 0880.34082

Buslaev, V.; Fedotov, A.

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau Sémin. 1993-1994, Exp. No. 21, 21 p. (1994).

The spectrum of the Harper equation \[ {\psi(x+ h)+ \psi(x-h)\over 2}+\cos x \psi(x)= E\psi(x) \] in \(L_2(\mathbb{R})\) is studied in the paper. The paper consists of two parts. In the first one the monodromization operation is described in general, and then it is applied to the Harper equation in the second part. Different theorems and lemmas are proved.

Reviewer: V.C.Boffi (Roma)

MSC:

34L05	General spectral theory of ordinary differential operators
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34M99	Ordinary differential equations in the complex domain

Keywords:

Harper equation; monodromization