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THE SPECTRUM OF A PARAMETRIZED PARTIAL DIFFERENTIAL OPERATOR OCCURRING IN HYDRODYNAMICS

Published online by Cambridge University Press:  24 March 2003

R. DENK ,
M. MÖLLER  and
C. TRETTER
R. DENK
Affiliation:
NWF I – Mathematik, University of Regensburg, D-93040 Regensburg, Germany; robert.denk@mathematik.uni-regensburg.de
M. MÖLLER
Affiliation:
Department of Mathematics, University of the Witwatersrand, 2050 WITS, South Africa; 036man@cosmos.wits.ac.za
C. TRETTER
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH; c.tretter@mcs.le.ac.uk
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Abstract

A partial differential operator associated with natural oscillations of an incompressible fluid in the neighbourhood of an elliptical flow is considered. The differentiation is only taken with respect to the angular variable, and thus the operator becomes a family of ordinary differential operators parametrized by the radial variable. It is shown that the spectra of these ordinary differential operators completely determine the spectrum of the given operator which turns out to have a kind of skeleton structure.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 483 - 492
Copyright
The London Mathematical Society, 2002

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