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:
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(2.1)
F is real-valued and absolutely continuous with respect to Lebesgue measure (dω) on T°
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(2.2)
F′ = f, which exists by (2.1), is a strictly positive, even, continuous density on T° which is of bounded variation
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(2.3)
0 < δ < f(ω) < Γ < ∞ for all ω ε [0, π] (δ and Γ fixed and independent of f and n)
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(2.4)
f has an absolutely convergent Fourier (cosine) series on [0, π].
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© 1983 Springer-Verlag New York Inc.
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Britton, W. (1983). Imposing the constraints. In: Conjugate Duality and the Exponential Fourier Spectrum. Lecture Notes in Statistics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5528-4_2
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DOI: https://doi.org/10.1007/978-1-4612-5528-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90826-7
Online ISBN: 978-1-4612-5528-4
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