 99191 Steve Clark, Fritz Gesztesy, Helge Holden, and Boris M. Levitan
 BorgType Theorems for MatrixValued Schr\"{o}dinger Operators
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May 21, 99

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Abstract. A Borgtype uniqueness theorem for matrixvalued Schr\"odinger operators is proved. More precisely, assuming a reflectionless potential matrix and spectrum
a halfline $[0,\infty)$, we derive triviality of the potential matrix. Our approach is based on trace formulas and matrixvalued Herglotz representation theorems. As a byproduct of our techniques, we obtain an extension of Borg's classical result from the class of periodic scalar potentials to the class of reflectionless matrixvalued potentials.
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