Abstract:
The wavelets and scaling functions based on Chebyshev polynomials and their zeros are introduced. The constructed system of functions is proved to be orthogonal. Using this system, an orthonormal basis in the space of square-integrable functions is built. Approximative properties of partial sums of corresponding wavelet series are investigated.
Key words:polynomial wavelets, Chebyshev polynomials of second kind, orthogonality, Christoffel–Darboux formula, function approximation, wavelet series.
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