Abstract
Wavelet theory has its origin in several disciplines; the types of functions that are now called wavelets were studied in quantum field theory, signal analysis, and function space theory. In all these areas, wavelet-like algorithms replaced the classical Fourier-type expansion of a function. It was not until the mid-1980s that these, at first, seemingly different notions were described in a unified manner. Because of the restricted scope of this monograph, we will not be able to address some ramifications of wavelet bases for so-called wavelet frames.
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