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Spectral theory for symmetric systems in an exterior domain. (English) Zbl 0655.35059

The author studies spectral problems for the operator \[ H(x,D)u=\sum^{n}_{j=1}A_ j(x)\partial u/\partial x_ j+C(x)u\quad (x\in \Omega) \] in an exterior domain \(\Omega\) of \({\mathbb{R}}^ n\); here \(u=(u_ 1,...,u_ d)\) is a \({\mathbb{C}}^ d\)-valued function, and \(A_ j\) and C are \(d\times d\)-matrix valued coefficients. The basic tool is the commutator method developed by E. Mourre [Commun. Math. Phys. 78, 391-408 (1981; Zbl 0489.47010)].
Reviewer: J.Appell

MSC:

35P05 General topics in linear spectral theory for PDEs
35F05 Linear first-order PDEs

Citations:

Zbl 0489.47010
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