Borg-Type Theorems for Matrix-Valued Schrödinger Operators

Steve Clark; Fritz Gesztesy; Helge Holden; Boris M. Levitan

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Borg-Type Theorems for Matrix-Valued Schrödinger Operators

Steve Clark·Fritz Gesztesy·Helge Holden·Boris M. Levitan

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Abstract

A Borg-type uniqueness theorem for matrix-valued Schrödinger 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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BibTeX RIS

Steve Clark, Fritz Gesztesy, Helge Holden, Boris M. Levitan. 1999-05-22. Borg-Type Theorems for Matrix-Valued Schrödinger Operators. https://arxiv.org/abs/math/9905143

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