Title

Wyle-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 Vel´azquez [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.

Department(s)

Mathematics and Statistics

Sponsor(s)

National Science Foundation (U.S.)

Keywords and Phrases

CMV Operators; Weyl-Titchmarsh Theory; Finite Difference Operators; Matrix-Valued Orthogonal Polynomials

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2007 Element, All rights reserved.

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