ABSTRACT
The field of Fourier analysis also includes the study of expansions of arbitrary func tions in bases other than the exponential functions or the trigonometric functions. One of our goals will be to adapt appropriate basic waveforms to each particular class of functions, so that the coefficients of the expansion convey maximal infor mation about the functions. To choose which bases are appropriate, it is necessary to establish some mathematical properties of those waveforms, such as their size, smoothness, orthogonality, and support. Some of these properties can best be de termined with classical methods involving the Fourier transform.
