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The algebraic-geometric AKNS potentials

Published online by Cambridge University Press:  19 September 2008

Corrado de Concini  and
Russell A. Johnson
Corrado de Concini
Affiliation:
Universita di Roma II, Roma, Italy
Russell A. Johnson
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
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Abstract

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We characterize the algebraic-geometric potentials for the Schrödinger and AKNS operators using the Weyl m-functions and the Floquet exponent for these operators. The characterization is this: among random ergodic Schrödinger operators, the alebraic-geometric potentials are those for which (i) the spectrum is a union of finitely many intervals (or bands); (ii) the Lyapounov exponent vanishes on the spectrum.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 1 , March 1987 , pp. 1 - 24
Copyright
Copyright © Cambridge University Press 1987

References

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