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].
Consider a stationary process X = {X([theta]) : [theta] [member of] [0, 2[pi])} with
Fourier expansionThe 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.
Secondly, we take
Fourier expansion of the residual r = f - g.