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Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle
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
Beurling-Malliavin theory for Toeplitz kernels
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
Reflectionless Herglotz Functions and Jacobi Matrices
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
Images of non-tangential sectors under Cauchy transforms
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
Spectral gaps for sets and measures
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
Two-spectra theorem with uncertainty
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).
On the distributions of boundary values of Cauchy integrals
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
Equivalence up to a rank one perturbation
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)
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