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Spectral analysis of fourth order differential operators I

✍ Scribed by Horst Behncke

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
218 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study the spectral theory of differential operators of the form

on ℒ^2^~w~ (0, ∞). By means of asymptotic integration, estimates for the eigenfunctions and__M__ ‐matrix are derived. Since the M ‐function is the Stieltjes transform of the spectral measure, spectral properties of τ are directly related to the asymptotics of the eigenfunctions. The method of asymptotic integration, however, excludes coefficients which are too oscillatory or whose derivatives decay too slowly. Consequently there is no singular continuous spectrum in all our cases. This was found earlier for Sturm–Liouville operators, for which theWKB method provides a good approximation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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