39 citations · 101 across the 14 of their papers we have counts for
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Remarks on Periodic Jacobi Matrices on Trees
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the…
Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices
Jacob S. Christiansen, Maxim Zinchenko
We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class complex perturbations of periodic and more generally finite gap Jacobi matric…
Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices
Jacob S. Christiansen, Maxim Zinchenko
We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class perturbations under very general assumptions. Our results apply, in particula…
Finite Gap Jacobi Matrices: A Review
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
A review of Finite Gap Jacobi Matrices.
Finite Gap Jacobi Matrices, III. Beyond the Szegő Class
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
Let $\fre\subset\bbR$ be a finite union of disjoint closed intervals and denote by the harmonic measure of the leftmost bands. The frequency module for $\fre$ is…
Finite Gap Jacobi Matrices, II. The Szegő Class
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
Let $\fre\subset\bbR$ be a finite union of disjoint closed intervals. We study measures whose essential support is $\fre$ and whose discrete eigenvalues obey a 1/2-power condition.…