Wyle-Titchmarsh Theory and Borg-Marchenko-type Uniqueness Results for CMV Operators with Matrix-valued Verblunsky Coefficients
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 Vel´azquez ) 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 matrixvalued Verblunsky coefficients as this is of independent interest and an essential ingredient in proving the corresponding Borg-Marchenko-type uniqueness theorems.
S. L. Clark et al., "Wyle-Titchmarsh Theory and Borg-Marchenko-type Uniqueness Results for CMV Operators with Matrix-valued Verblunsky Coefficients," Operators and Matrices, Element, Jan 2007.
Mathematics and Statistics
National Science Foundation (U.S.)
Keywords and Phrases
CMV Operators; Weyl-Titchmarsh Theory; Finite Difference Operators; Matrix-Valued Orthogonal Polynomials
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01 Jan 2007