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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Essential spectrum of a system of singular differential operators and the asymptotic Hain-Lüst operator


Authors: Reinhard Mennicken, Serguei Naboko and Christiane Tretter
Journal: Proc. Amer. Math. Soc. 130 (2002), 1699-1710
MSC (1991): Primary 47A10, 47B25, 76W05
Published electronically: December 20, 2001
MathSciNet review: 1887017
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Abstract: We consider a matrix differential operator with singular entries which arises in magnetohydrodynamics. By means of the asymptotic Hain-Lüst operator and some pseudo-differential operator techniques, we determine the essential spectrum of this operator. Whereas in the regular case, the essential spectrum consists of two intervals, it turns out that in the singular case two additional intervals due to the singularity may arise. In addition, we establish criteria for the essential spectrum to lie in the left half-plane.


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Additional Information

Reinhard Mennicken
Affiliation: NWF I – Mathematik, University of Regensburg, D-93040 Regensburg, Germany
Email: reinhard.mennicken@mathematik.uni-regensburg.de

Serguei Naboko
Affiliation: Department of Mathematical Physics, Institute for Physics, St. Petersburg University, ul. Ulianovskaja 1, 198904 St. Petergoff, St. Petersburg, Russia
Email: naboko@snoopy.phys.spbu.ru

Christiane Tretter
Affiliation: Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
Email: c.tretter@mcs.le.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06239-6
PII: S 0002-9939(01)06239-6
Received by editor(s): May 3, 2000
Received by editor(s) in revised form: December 5, 2000
Published electronically: December 20, 2001
Additional Notes: The authors acknowledge the support of the Regensburger Universitätsstiftung Hans Vielberth.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society