4 citations · 9 across the 4 of their papers we have counts for
4 papers
Reflectionless Herglotz functions and generalized Lyapunov exponents
Alexei Poltoratski, Christian Remling
We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss…
Pseudocontinuation and cyclicity for random power series
Evgeny Abakumov, Alexei Poltoratski
We prove that a random function in the Hardy space is a non-cyclic vector for the backward shift operator almost surely. The question of existence of a local pseudocontinuati…
Uniqueness theorems for Cauchy integrals
Mark Melnikov, Alexei Poltoratski, Alexander Volberg
If is a finite complex measure in the complex plane $\C$ we denote by its Cauchy integral defined in the sense of principal value. The measure is called reflectionles…
Beurling-Malliavin theory for Toeplitz kernels
N. Makarov, A. Poltoratski
We consider the family of Toeplitz operators acting in the Hardy space in the upper halfplane; and are given meromorphic inner functions, and is…