Titlebook: Conjugate Duality and the Exponential Fourier Spectrum; Wray Britton Book 1983 Springer-Verlag New York Inc. 1983 Duality.Dualit?t (Math.)

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DEAF

Selecting the objective functional: conjugate duality,Observe that for . n there are an infinity of spectral densities in which in particular satisfy (2.7). In order to select a unique function from Ω. we need a criterion. Putting aside certain philosophical issue (Jaynes, 1979), consider the negentropy functional:.H:Ω. → R, where:..

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Scintillations

Solving for ,By Theorem 3.16, . is determined by the following relation:.,.where Z. (θ .) = 2π(c*c). and:

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Obtaining an initial estimate , of ,Consider the . ., where:...and . consists of n+1 Lagrange multipliers.

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Numerical asymptotics,I begin with some classical motivational results:. (F. and M. Riesz; cf. Koosis, 1980, pp. 40–47/100–102) Let F be a spectral distribution which is of bounded variation on T.. Let r. denote the k. trigonometric moment of the measure dF, i.e.,...If ., then F is absolutely continuous.

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Conclusion,From the numerical experiment, we see that it is feasible to reconstruct a sufficiently smooth spectral density on the basis of the minimum negentropy criterion. We achieve a robust spectral density estimator in f. at the expense of increased computational complexity and the possible degradation of the statistical asymptotic properties of ..

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Transportrecht - Schnell erfasstrical work, we must employ the functional . and {c., 0 ≤ k ≤ N.} is determined by recursive relation (3.16.3)-(3.16.4) for some judicious truncation point N. ≤ ∞. Recall that {r.,1 ≤ k ≤ n} is given for n ≤ N.