具有矩阵值Verblunsky系数的CMV算子的Weyl-Titchmarsh理论和Borg-Marchenko型唯一性结果
Weyl-Titchmarsh Theory and Borg-Marchenko-type Uniqueness Results for CMV Operators with Matrix-Valued Verblunsky Coefficients
摘要：
我们证明了局部和全球版本的Borg-Marchenko型唯一性定理的半格和全格CMV运营商（CMV的Canadian，道德，Velazquez）与矩阵值Verblunsky系数。虽然我们的半格的结果制定的矩阵值Weyl-Titchmarsh函数，我们的全格的结果涉及对角和主要的非对角格林矩阵。我们还开发了基础的Weyl-Titchmarsh理论的CMV运营商与矩阵值Verblunsky系数，因为这是独立的利益和必要的成分，证明相应的Borg-Marchenko型唯一性定理。
英文摘要：
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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