Borg-Type Theorems for Matrix-Valued Schrödinger Operators

Details Borg-Type Theorems for Matrix-Valued Schrödinger Operators Borg-Type Theorems for Matrix-Valued Schrödinger Operators

1999-05-22

arxiv.org/abs/math/9905143v1

Mathematics

Spectral Theory

LaTeX, 22 pages

Scientific paper

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.

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