43 citations · 194 across the 50 of their papers we have counts for
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The Deift Conjecture: A Program to Construct a Counterexample
David Damanik, Milivoje Lukić, Alexander Volberg +1
We describe a program to construct a counterexample to the Deift conjecture, that is, an almost periodic function whose evolution under the KdV equation is not almost periodic in t…
Kotani-Last problem and Hardy spaces on surfaces of Widom type
A. Volberg, P. Yuditskii
It is a small theory of non almost periodic ergodic families of Jacobi matrices with pure (however) absolutely continuous spectrum. And the reason why this effect may happen: under…
Remarks on Nehari's problem, matrix condition, and weighted bounded mean oscillation
A. Volberg, P. Yuditskii
We consider Nehari's problem in the case of non-uniqueness of solution. The solution set is then parametrized by the unit ball of by means of so-called {\em regular ge…
Reflectionless measures with a point mass and singular continuous component
F. Nazarov, A. Volberg, P. Yuditskii
We construct mesures supported on a compact subset E of the real line having zero principal value of their Cauchy integral a.e. on E with respect to Lebesgue measure and having sin…
Inverse scattering problem for a special class of canonical systems and non-linear Fourier integral. Part I: asymptotics of eigenfunctions
S. Kupin, F. Peherstorfer, A. Volberg +1
An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (i…
Limit periodic Jacobi matrices with a singular continuous spectrum and the renormalization of periodic matrices
F. Peherstorfer, A. Volberg, P. Yuditskii
Our main result asserts that a certain natural non-linear operator on Jacobi matrices built by a hyperbolic polynomial with real Julia set is a contraction in operator norm if the…
Asymptotics of orthogonal polynomials via the Koosis theorem
F. Nazarov, A. Volberg, P. Yuditskii
The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by p…