64 citations · 236 across the 39 of their papers we have counts for
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The Hilbert Transform of a Measure
Alexei Poltoratski, Barry Simon, Maxim Zinchenko
Let $\fre$ be a homogeneous subset of in the sense of Carleson. Let be a finite positive measure on and its Hilbert transform. We prove that if $\lim_{t\…
Finite Gap Jacobi Matrices, I. The Isospectral Torus
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
Let be a finite union of disjoint closed intervals. In the study of OPRL with measures whose essential support is , a fundamental role is play…
Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients
Maxim Zinchenko
We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez) associated with matrix-valued Verblunsky coef…
Essential Closures and AC Spectra for Reflectionless CMV, Jacobi, and Schrödinger Operators Revisited
Fritz Gesztesy, Konstantin A. Makarov, Maxim Zinchenko
We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of…
Borg-Marchenko-type Uniqueness Results for CMV Operators
Stephen Clark, Fritz Gesztesy, Maxim Zinchenko
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 \cite{CMV03}).…
Local Spectral Properties of Reflectionless Jacobi, CMV, and Schrödinger Operators
Fritz Gesztesy, Maxim Zinchenko
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition…