Approximative properties of the Chebyshev wavelet series of the second kind. (Russian. English summary) Zbl 1474.42146

Summary: 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.


42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42A10 Trigonometric approximation
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
41A99 Approximations and expansions
Full Text: MNR


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