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Abstract
A general approach through a multiresolution analysis is given for the construction of orthonormal and Riesz wavelet bases in a separable Hilbert space of functions. The method builds upon an appropriate orthonormal basis of the Hilbert space. It is applied to several Hilbert spaces of interest, unifying known examples and also generating new examples. Specific cases considered are periodic functions over the real line, analytic functions on the unit disk and functions generated by Chebyshev polynomials.
†Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday.
Notes
†Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday.