Sharp Bounds on the Number of Resonances for Symmetric Systems Ii. Non-compactly Supported Perturbations
نویسندگان
چکیده
We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems. The purpose of this note is to extend the results obtained in [5] to non-compactly supported perturbations. Consider in R, n ≥ 3 odd, a first order matrix-valued differential operator of the form ∑n j=1A 0 jDxj , A 0 j being constant Hermitian d× d matrices, and denote by G0 its selfadjoint realization on H = L 2(R;C). Suppose that the matrix A(ξ) = ∑n j=1A 0 jξj, ξ ∈ R n \ 0, is invertible for all ξ, i.e. the operator G0 is an elliptic one. Consider the operator ∑n j=1Aj(x)Dxj +B(x), where Aj(x) ∈ C 1(R,C), B(x) ∈ C0(R,C) satisfy for |x| ≫ 1: n
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