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

Mennicken, Reinhard; Naboko, Serguei; Tretter, Christiane

doi:10.1090/S0002-9939-01-06239-6

Essential spectrum of a system of singular differential operators and the asymptotic Hain–Lüst operator
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by Reinhard Mennicken, Serguei Naboko and Christiane Tretter PDF

Proc. Amer. Math. Soc. 130 (2002), 1699-1710 Request permission

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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