 04243 Steve Clark, Fritz Gesztesy, and Walter Renger
 Trace Formulas and BorgType Theorems for MatrixValued Jacobi and Dirac
Finite Difference Operators
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Aug 4, 04

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Abstract. Borgtype uniqueness theorems for matrixvalued Jacobi operators
H and supersymmetric Dirac difference operators D are proved. More
precisely, assuming reflectionless matrix coefficients A, B in the
selfadjoint Jacobi operator H=AS^+ + A^S^ + B (with S^\pm the
right/left shift operators on the lattice Z) and the
spectrum of H to be a compact interval [E_,E_+], $E_ < E_+, we
prove that A and B are certain multiples of the identity matrix. An
analogous result which, however, displays a certain novel
nonuniqueness feature, is proved for supersymmetric selfadjoint Dirac
difference operators D with spectrum given by
[E_+^{1/2},E_^{1/2}] \cup [E_^{1/2},E_+^{1/2}], 0 \leq E_ < E_+.
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