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Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle

- N. Makarov, A. Poltoratski
- Mathematics
- 2005

This paper touches upon several traditional topics of 1D linear complex analysis
including distribution of zeros of entire functions, completeness problem for
complex exponentials and for other… Expand

Beurling-Malliavin theory for Toeplitz kernels

- N. Makarov, A. Poltoratski
- Mathematics
- 16 February 2007

AbstractWe consider the family of Toeplitz operators
$T_{J\bar{S}^{a}}$
acting in the Hardy space H2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real… Expand

Reflectionless Herglotz Functions and Jacobi Matrices

- A. Poltoratski, C. Remling
- Mathematics
- 1 June 2009

We study several related aspects of reflectionless Jacobi matrices. First, we discuss the singular part of the corresponding spectral measures. We then show how to identify sets on which measures are… Expand

Boundary convergence of vector-valued pseudocontinuable functions☆

- V. Kapustin, A. Poltoratski
- Mathematics
- 1 September 2006

Images of non-tangential sectors under Cauchy transforms

- A. Poltoratski
- Mathematics
- 1 December 2003

Let μ be a complex measure on the circle. We denote byPμ andQμ the Poisson and conjugate Poisson integrals of μ in the unit disk, respectively. In this note, we study the relative asymptotic growth… Expand

Polya sequences, Toeplitz kernels and gap theorems

- Mishko Mitkovski, A. Poltoratski
- Mathematics
- 26 March 2009

Spectral gaps for sets and measures

- A. Poltoratski
- Mathematics
- 14 August 2009

If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum of a measure, taken over all non-trivial finite complex measures supported on X. In… Expand

Two-spectra theorem with uncertainty

- N. Makarov, A. Poltoratski
- MathematicsJournal of Spectral Theory
- 15 December 2016

The goal of this paper is to combine ideas from the theory of mixed spectral problems for differential operators with new results in the area of the Uncertainty Principle in Harmonic Analysis (UP).… Expand

On the distributions of boundary values of Cauchy integrals

- A. Poltoratski
- Mathematics
- 1 August 1996

We use new methods to give short proofs to some known results on the distributions of boundary values of Cauchy integrals. We also indicate some further generalizations. INTRODUCTION Let W be an… Expand

Equivalence up to a rank one perturbation

- A. Poltoratski
- Mathematics
- 1 May 2000

This note is devoted to the spectral analysis of rank one perturbations of unitary and self-adjoint operators. We study the following question: given two cyclic (i.e., having simple spectrum)… Expand

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