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]].

A note on the non-vanishing of Poincare series for the Fricke group [[GAMMA].sup.+.sub.0](p)

LUBICH, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, Arch.

ASYMPTOTIC CONSISTENT EXPONENTIAL-TYPE INTEGRATORS FOR KLEIN-GORDON-SCHRODINGER SYSTEMS FROM RELATIVISTIC TO NON-RELATIVISTIC REGIMES

Convergence acceleration of the modified Fourier expansions by means of rational corrections was considered in [6].

Optimal Rational Approximations by the Modified Fourier Basis

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).

Reconstruccion de senales periodicas usando redes neuronales

Consider a stationary process X = {X([theta]) : [theta] [member of] [0, 2[pi])} with Fourier expansion

Levy-based error prediction in circular systematic sampling

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).

On the eigenfunctions of the finite Hankel transform

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]).

The center restored: Chicago's residential price gradient reemerges

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.

An Inquest of Non-Linear Pulsations in Bq Serpens and VX Puppis

Every holomorphic automorphic form on [G.sub.n]([A.sub.F]) has a Fourier expansion in the following sense.

On the linear representability of Siegel-Hilbert modular forms by theta series

The Fourier expansion of the square wave from a 1-bit DRFM is:

Spur levels in multiple-bit DRFMs

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.

Parallel Solution Methods and Preconditioners for Evolution Equations

Secondly, we take Fourier expansion of the residual r = f - g.

Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients