Weyl-Titchmarsh theory and Borg-Marchenko-type uniqueness results for CMV operators with matrix-valued Verblunsky coefficients

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 [19]) 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. Mathematics subject classification (2000): Primary 34E05, 34B20, 34L40; Secondary 34A55.