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Imposing the constraints

  • Wray Britton
Part of the Lecture Notes in Statistics book series (LNS, volume 18)

Abstract

Let Ωn# denote the parental function space for Ωn consisting of all spectral distribution functions F on the torus T° = [-Π, Π] endowed with the Lebesgue σ-algebra T which satisfy the following constraints:
  1. (2.1)

    F is real-valued and absolutely continuous with respect to Lebesgue measure (dω) on T°

     
  2. (2.2)

    F′ = f, which exists by (2.1), is a strictly positive, even, continuous density on T° which is of bounded variation

     
  3. (2.3)

    0 < δ < f(ω) < Γ < ∞ for all ω ε [0, π] (δ and Γ fixed and independent of f and n)

     
  4. (2.4)

    f has an absolutely convergent Fourier (cosine) series on [0, π].

     

Keywords

Hilbert Space Harmonic Function Lebesgue Measure Unit Disk Topological Group 
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. 1983

Authors and Affiliations

  • Wray Britton

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