Best Approximation by Analytic and Meromorphic Functions

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


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
$$\left\| {\varphi - f} \right\|{L^{\infty }} = \left\| {{H_{\varphi }}} \right\| $$
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 ).


Toeplitz Operator Besov Space Trigonometric Polynomial Hankel Operator Constant Modulus 
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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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