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Parametrization of Solutions of the Nehari Problem

  • Vladimir Peller
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

For a Hankel operator Γ from H2 to H2 and p ≥ ||Γ||, we consider in this section the problem of describing all symbols φL of Γ (i.e., Γ = H φ ) which satisfy the inequality ||φ||∞ ≤ p. If φ0 is a symbol of F, then as we have seen in §1.1, this problem is equivalent to the problem of finding all approximants fH to φ0 satisfying ||φ0 — f|| . ≤ p. This problem is called the Nehari problem. If p = ||Γ||, a solution yo of the Nehari problem (i.e., a symbol φ of Γ of norm at most φ is called optimal. If p > ||Γ||, the solutions of the Nehari problem are called suboptimal). Clearly, the optimal solutions of the Nehari problem are the symbols of F of minimal norm.

Keywords

Unit Ball Toeplitz Operator Canonical Function Minimal Norm Blaschke Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 2003

Authors and Affiliations

  • Vladimir Peller
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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