Weyl-Titchmarsh theory and Borg-Marchenko-type uniqueness results for CMV operators with matrix-valued Verblunsky coefficients
نویسندگان
چکیده
منابع مشابه
Borg–marchenko-type Uniqueness Results for Cmv Operators
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 Velázquez [15]). While our half-lattice results are formulated in terms of Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s functions.
متن کاملTrace Formulas and a Borg-type Theorem for Cmv Operators with Matrix-valued Coefficients
We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez [13]) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result [39...
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Relations between halfand full-lattice CMV operators with scalarand matrix-valued Verblunsky coefficients are investigated. In particular, the decoupling of full-lattice CMV operators into a direct sum of two half-lattice CMV operators by a perturbation of minimal rank is studied. Contrary to the Jacobi case, decoupling a full-lattice CMV matrix by changing one of the Verblunsky coefficients re...
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We systematically develop Weyl–Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type
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We explicitly determine the high-energy asymptotics for Weyl– Titchmarsh matrices associated with general Dirac-type operators on half-lines and on R. We also prove new local uniqueness results for Dirac-type operators in terms of exponentially small differences of Weyl–Titchmarsh matrices. As concrete applications of the asymptotic high-energy expansion we derive a trace formula for Dirac oper...
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ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2007
ISSN: 1846-3886
DOI: 10.7153/oam-01-31