99-191 Steve Clark, Fritz Gesztesy, Helge Holden, and Boris M. Levitan

Borg-Type Theorems for Matrix-Valued Schr\"{o}dinger Operators (78K, LaTeX) May 21, 99

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. A Borg-type uniqueness theorem for matrix-valued Schr\"odinger operators is proved. More precisely, assuming a reflectionless potential matrix and spectrum a half-line $[0,\infty)$, we derive 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.

Files: 99-191.tex