Imposing the constraints

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


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].



Hilbert Space Harmonic Function Lebesgue Measure Unit Disk Topological Group 
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Copyright information

© Springer-Verlag New York Inc. 1983

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  • Wray Britton

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