Borg-type theorems for matrix-valued Schrodinger operators

A Borg-type uniqueness theorem for matrix-valued Schrodinger operators is p roved. More precisely, assuming a reflectionless potential matrix and its s pectrum a half-line [0, infinity). we derive the triviality of the potentia l matrix. Our approach is based on trace formulas and matrix-valued Herglot z representation theorems. As a by-product of our techniques, we obtain an extension of Borg's classical result From the class of periodic scalar pote ntials to the class of reflectionless matrix-valued potentials. (C) 2000 Ac ademic Press.