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Best Approximation by Analytic and Meromorphic Functions

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

Abstract

Let φ be a function on 𝕋 of class BMO. As we have already discussed in Chapter 1, there exists a function fBMOA such that φ — fL (𝕋) and
$$\left\| {\varphi - f} \right\|{L^{\infty }} = \left\| {{H_{\varphi }}} \right\| $$
(0.1)
Such a function f is called a best approximation to φ by analytic functions in L . We have already seen in §1.1 that in general a best approximation is not unique (see Theorem 5.1.5, which gives a necessary and sufficient condition for uniqueness in terms of the Hankel operator ).

Keywords

Toeplitz Operator Besov Space Trigonometric Polynomial Hankel Operator Constant Modulus 
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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