Borg-Type Theorems for Matrix-Valued Schrödinger Operators

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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.
LaTeX, 22 pages

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Spectral Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/78546

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9905143
 http://arxiv.org/abs/math/9905143

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arXiv