Abstract
A simple and explicit construction of an orthnormal trigonometric polynomial basis in the spaceC of continuous periodic functions is presented. It consists simply of periodizing a well-known wavelet on the real line which is orthonormal and has compactly supported Fourier transform. Trigonometric polynomials resulting from this approach have optimal order of growth of their degrees if their indices are powers of 2. Also, Fourier sums with respect to this polynomial basis are projectors onto subspaces of trigonometric polynomials of high degree, which implies almost best approximation properties.
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Communicated by Ronald A. DeVore.
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Offin, D., Oskolkov, K. A note on orthonormal polynomial bases and wavelets. Constr. Approx 9, 319–325 (1993). https://doi.org/10.1007/BF01198009
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DOI: https://doi.org/10.1007/BF01198009