Parametrization of Solutions of the Nehari Problem

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


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.


Unit Ball Toeplitz Operator Canonical Function Minimal Norm Blaschke Product 
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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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