Borg-type theorems for matrix-valued Schrodinger operators

[摘要] A Borg-type uniqueness theorem for matrix-valued Schrodinger operators is proved. More precisely, assuming a reflectionless potential matrix and its spectrum a half-line [0, infinity). we derive the triviality of the potential matrix. Our approach is based on trace formulas and matrix-valued Herglotz representation theorems. As a by-product of our techniques, we obtain an extension of Borg's classical result From the class of periodic scalar potentials to the class of reflectionless matrix-valued potentials. (C) 2000 Academic Press.

[发布日期] 2000-10-10