A remark on the reproducing kernel thesis for Hankel operators

@article{Treil2011ARO,
  title={A remark on the reproducing kernel thesis for Hankel operators},
  author={Sergei Treil},
  journal={arXiv: Functional Analysis},
  year={2011}
}
  • 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… 
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