From high oscillation to rapid approximation I: Modified Fourier expansions

In this paper we consider a modification of the classical Fourier expansio n, whereby in ( 1, 1) the sinnx functions are replaced by sin�(n 1 )x, n � 1. This has a number of important advantages in the approximation of analytic, nonperiodic functions. In particular, expansion coefficients decay like O n 2 � , rather than like O n 1 � . We explore theoretical features of these modified Fourier expansions, prove suitable versions of Fej´

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