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Essential spectrum of a system of singular differential operators and the asymptotic Hain-Lüst operator
Author(s):
Reinhard
Mennicken;
Serguei
Naboko;
Christiane
Tretter
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1699-1710.
MSC (1991):
Primary 47A10, 47B25, 76W05
Posted:
December 20, 2001
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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.
References:
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- Descloux, J., Geymonat, G., Sur le spectre essentiel d'un operateur relatif à la stabilité d'un plasma en géometrie toroïdale, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), 795-797. MR 81e:76087
- [FMM1]
- Faierman, M., Mennicken, R., Möller, M., The essential spectrum of a system of singular ordinary differential operators of mixed order. Part I: The general problem and an almost regular case, Math. Nachr. 208 (1999), 101-115. MR 2000i:34156
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- Faierman, M., Mennicken, R., Möller, M., The essential spectrum of a system of singular ordinary differential operators of mixed order. Part II: The generalization of Kako's problem, Math. Nachr. 209 (2000), 55-81. MR 2000i:34155
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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:
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
Posted:
December 20, 2001
Additional Notes:
The authors acknowledge the support of the Regensburger Universitätsstiftung Hans Vielberth.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2001,
American Mathematical Society
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