m at h . SP ] 7 F eb 2 00 1 UNIQUENESS RESULTS FOR MATRIX - VALUED SCHRÖDINGER , JACOBI , AND DIRAC - TYPE OPERATORS
نویسندگان
چکیده
Let g(z, x) denote the diagonal Green's matrix of a self-adjoint m × m matrix-valued Schrödinger operator H = − d 2 dx 2 Im + Q(x) in L 2 (R) m , m ∈ N. One of the principal results proven in this paper states that for a fixed x 0 ∈ R and all z ∈ C + , g(z, x 0) and g ′ (z, x 0) uniquely determine the matrix-valued m × m potential Q(x) for a.e. x ∈ R. We also prove the following local version of this result. Let g j (z, x), j = 1, 2 be the diagonal Green's matrices of the self-adjoint Schrödinger operators H j = −
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0 v 1 [ m at h . SP ] 1 9 A pr 2 00 0 UNIQUENESS RESULTS FOR MATRIX - VALUED SCHRÖDINGER , JACOBI , AND DIRAC - TYPE OPERATORS
Let g(z, x) denote the diagonal Green's matrix of a self-adjoint m × m matrix-valued Schrödinger operator H = − d 2 dx 2 Im + Q(x) in L 2 (R) m , m ∈ N. One of the principal results proven in this paper states that for a fixed x 0 ∈ R and all z ∈ C + , g(z, x 0) and g ′ (z, x 0) uniquely determine the matrix-valued m × m potential Q(x) for a.e. x ∈ R. We also prove the following local version o...
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