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SPECTRAL ANALYSIS OF HIGHER-ORDER DIFFERENTIAL OPERATORS II: FOURTH-ORDER EQUATIONS

Published online by Cambridge University Press:  01 February 1999

CHRISTIAN REMLING
CHRISTIAN REMLING
Affiliation:
FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany. E-mail: [email protected]
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Abstract

We investigate the location and nature of the spectrum of the fourth-order self-adjoint equation

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subject to certain asymptotic assumptions on the coefficients. The main tools are the theory of asymptotic integration and the Titchmarsh–Weyl M-matrix. Asymptotic integration yields asymptotic formulae for the solutions of the differential equation which are then used to derive properties of the M-matrix. The characterisation of spectral properties in terms of the boundary behaviour of M leads to the desired results.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 188 - 206
Copyright
The London Mathematical Society 1999

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