Abstract
Spectral representations of the dilation and translation operators on L 2(ℝ) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.
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Gómez-Cubillo, F., Suchanecki, Z. Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of L 2(ℝ). J Fourier Anal Appl 17, 191–225 (2011). https://doi.org/10.1007/s00041-010-9148-z
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DOI: https://doi.org/10.1007/s00041-010-9148-z