Characteristic Wavelet Equations and Generalizations of the Spectral Function
Two equations characterize orthonormal (and Parseval) wavelets in L2(ℝ). We trace the history and development of this characterization and present a different argument that uses a generalization of the spectral function of Bownik and Rzeszotnik. By further generalizing this function in the setting of an abstract Hilbert space, we present a compressed proof of the abstract characteristic equation.
KeywordsSpectral Function Orthonormal Wavelet Multiplicity Function Parseval Frame Countable Collection
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