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arXiv · 1002.0387

Weyl-Titchmarsh Theory and Borg-Marchenko-type Uniqueness Results for CMV Operators with Matrix-Valued Verblunsky Coefficients

Stephen Clark·Fritz Gesztesy·Maxim Zinchenko
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Abstract

We prove local and global versions of Borg-Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velazquez) with matrix-valued Verblunsky coefficients. While our half-lattice results are formulated in terms of matrix-valued Weyl-Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green's matrices. We also develop the basics of Weyl-Titchmarsh theory for CMV operators with matrix-valued Verblunsky coefficients as this is of independent interest and an essential ingredient in proving the corresponding Borg-Marchenko-type uniqueness theorems.

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Stephen Clark, Fritz Gesztesy, Maxim Zinchenko. 2010-02-02. Weyl-Titchmarsh Theory and Borg-Marchenko-type Uniqueness Results for CMV Operators with Matrix-Valued Verblunsky Coefficients. https://arxiv.org/abs/1002.0387

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