A remark on the reproducing kernel thesis for Hankel operators

  title={A remark on the reproducing kernel thesis for Hankel operators},
  author={Sergei Treil},
  journal={arXiv: Functional Analysis},
  • S. Treil
  • Published 30 December 2011
  • Mathematics
  • arXiv: Functional Analysis
A simple proof is given of the so-called reproducing kernel thesis for Hankel operators. Notation := equal by definition; C the complex plane; D the unit disk, D := {z ∈ C : |z| < 1}; T the unit circle, T := ∂D = {z ∈ C : |z| = 1}; p f(n) Fourier coefficient of the function f , p f(n) := (2π)−1 ∫ T f(z)z−n |dz|; L = L(T) Lebesgue spaces with respect to the normalized Lebesgue measure (2π)−1|dz| on T; H Hardy spaces, H := {f ∈ L(T) : p f(n) = 0 ∀n < 0}; H − H 2 − := L (T) H = {f ∈ L(T) : p f(n… 
11 Citations
A boundedness criterion for singular integral operators of convolution type on the Fock space
We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, the integral operator \begin{eqnarray*}
Normal Truncated Toeplitz Operators
The characterization of normal truncated Toepltiz operators is first given by Chalendar and Timotin. We give an elementary proof of their result without using the algebraic properties of truncated


Weighted interpolation in Paley-Wiener spaces and finite-time controllability
This paper considers the solution of weighted interpolation problems in model subspaces of the Hardy space H-2 that are canonically isometric to Paley-Wiener spaces of analytic functions A new
Carleson potentials and the reproducing kernel thesis for embedding theorems
In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball. The only technical tool used in the proof of this fact is Green's formula. The starting point is
Treatise on the shift operator : spectral function theory
Introductory Lecture. What This Book is About.- 1. Basic Objects.- 2. The Functional Model.- 3. The Details of the Plan.- 4. Concluding Remarks.- Lecture I. Invariant Subspaces.- 1. The Fundamental
Hankel operators on the
Nikol′skĭı, Treatise on the shift operator, Grundlehren der Mathematischen Wissenschaften [Fundamental
  • Principles of Mathematical Sciences],
  • 1986
Boundedness of Hankel Matrices
Hankel operators, embedding theorems and bases of coinvariant subspaces of the multiple shift operator
  • MR1047967 (91f:47014) Department of Mathematics
  • 1917