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Monodromization and the Harper equation. (English) Zbl 0880.34082

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
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