@MISC{Wickerhauser92smoothlocalized, author = {Mladen Victor Wickerhauser}, title = {Smooth Localized Orthonormal Bases}, year = {1992} }

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Abstract

. We describe an orthogonal decomposition of L 2 (R) which maps smooth functions to smooth periodic functions. It generalizes previous constructions by Malvar, Coifman and Meyer. The adjoint of the decomposition can be used to construct smooth orthonormal windowed exponential, wavelet and wavelet packet bases. Orthogonal projections which map smooth functions to smooth compactly supported functions appeared in the work of Malvar [M] and Coifman and Meyer [CM]. In those papers the projections were used to build a smooth overlapping orthogonal basis on the line, composed of windowed sine (or cosine) functions. Many of these bases' properties were only briefly described in the short papers of Malvar, Coifman, and Meyer, but are developed in detail in [AWW]. We do not wish to overlook the original sources, but we will take advantage of some of the later paper's structure and notation. In this short note we sketch a construction of smoothness-preserving unitary maps onto periodic function...