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CORRESPONDENCE OF THE EIGENVALUES OF A NON-SELF-ADJOINT OPERATOR TO THOSE OF A SELF-ADJOINT OPERATOR

Part of: Boundary value problems

Published online by Cambridge University Press:  13 July 2010

John Weir
John Weir*
Affiliation:
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, U.K. (email: [email protected])
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Abstract

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues.

MSC classification

Secondary: 34B24: Sturm-Liouville theory
Type
Research Article
Information
Mathematika , Volume 56 , Issue 2 , July 2010 , pp. 323 - 338
Copyright
Copyright © University College London 2010

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