Precursors in Mathematics: Early Wavelet Bases


The plain fact that wavelet families are very interesting orthonormal systems for L(R) makes it natural to view them as an important contribution to the field of orthogonal expansions of functions. This classical field of mathematical analysis was particularly flourishing in the first 30 years of the 20th century, when detailed discussions of the convergence of orthogonal series, in particular of trigonometric series, were undertaken. Alfred Haar describes the situation in his 1910 paper in Math. Annalen appropriately as follows: for any given (family of) orthonormal system(s) of functions on the unit interval [0, 1] one has to ask the following questions:

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@inproceedings{FeichtingerPrecursorsIM, title={Precursors in Mathematics: Early Wavelet Bases}, author={Hans G. Feichtinger} }