Fourier expansion


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Fourier expansion

[‚fu̇r·ē‚ā ik′span·chən]
(mathematics)
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Recalling (2) and (3), in order to express the Fourier expansion explicitly, we need to find representatives of the double coset [[GAMMA].sub.[infinity]] \ [[GAMMA].sup.+.sub.0(p)/ [[GAMMA].sub.[infinity]].
LUBICH, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, Arch.
Convergence acceleration of the modified Fourier expansions by means of rational corrections was considered in [6].
The comparison between the Fourier neural network in equation (5) and the Fourier expansion in equation (2) shows that [b.sub.0] is equivalent to [a.sub.0]; also [[omega].sub.n] to mm; and [b.sub.n] to 0 or 7[pi]/2; finally, [a.sub.n] in equation (5) is equivalent to the coefficients [a.sub.n] y [b.sub.n] in equation (2).
Consider a stationary process X = {X([theta]) : [theta] [member of] [0, 2[pi])} with Fourier expansion
The proposition below shows that the contribution from [T.sub.l] at indices l > L in the Fourier expansion of h [member of] [R.sub.g] ([K.sub.am]) is at most [[??].sub.L+1] as large as that in the associated function G = [[K.sup.-1].sub.am] (h).
Following Gallant (1981, 1982), McMillen and Dombrow (2001) use a Fourier expansion to model g([T.sub.t]) and g([T.sup.s.sub.t]).
Performing Fourier expansion, we have refined the fundamental frequency of pulsation for BQ Serpens to be 0.2341 c/d and the first overtone to 0.3320 c/d.
Every holomorphic automorphic form on [G.sub.n]([A.sub.F]) has a Fourier expansion in the following sense.
The Fourier expansion of the square wave from a 1-bit DRFM is:
Utilizing the Fourier expansion representation, as we show in the sequel, enables us to strongly increase the degree of parallelism of the underlying solution methods.