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SPECTRAL THEORY OF HIGHER ORDER DIFFERENTIAL OPERATORS

Published online by Cambridge University Press:  19 December 2005

HORST BEHNCKE
HORST BEHNCKE
Affiliation:
Department of Mathematics, University of Osnabrück, 49069 Osnabrück, Germanybehncke@mathematik.uni-osnabrueck.de
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Abstract

The absolutely continuous spectrum of a very general class of differential operators of order $2n$ is determined, for operators whose coefficients satisfy conditions that combine smoothness and decay properties. The main methods are asymptotic integration and the analysis of the associated $M$-matrix. The form of the solutions precludes the absence of a singular continuous spectrum.

Keywords

absolutely continuous spectrumM-matrixasymptotic integration34L0547E05
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 1 , January 2006 , pp. 139 - 160
Copyright
2006 London Mathematical Society

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