Advertisement

Journal of Mathematical Sciences

, Volume 243, Issue 6, pp 880–894 | Cite as

Kernels of Toeplitz Operators and Rational Interpolation

  • V. V. KapustinEmail author
Article
  • 5 Downloads

The kernel of a Toeplitz operator on the Hardy class H2 in the unit disk is a nearly invariantsubspace of the backward shift operator, and, by D. Hitt’s result, it has the form g · Kω where ω is an inner function, Kω = H2ωH2, and g is an isometric multiplier on Kω. We describe the functions ω and g for the kernel of the Toeplitz operator with symbol .\( \overline{\theta}\varDelta \) where θ is an inner function and Δ is a finite Blaschke product.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Hitt, “Invariant subspaces of \( {\mathcal{H}}^2 \) of an annulus,” Pacific J. Math., 134, No. 1, 101–120 (1988).Google Scholar
  2. 2.
    R. Nevanlinna, “Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen,” Ann. Acad. Sci. Fenn. Ser. A, 13, No. 1 (1920).Google Scholar
  3. 3.
    E. Hayashi, “Classification of nearly invariant subspaces of the backward shift,” Proc. Amer. Math. Soc., 110, No. 2, 441–448 (1990).MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. B. Crofoot, “Multipliers between invariant subspaces of the backward shift,” Pacific J. Math., 166, No. 2, 225–246 (1994).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St.Petersburg Department of Steklov Institute of MathematicsSt.PetersburgRussia

Personalised recommendations