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

Sultanakhmedov, Murad Salikhovich

Vladikavkaz. Mat. Zh. 17, No. 3, 56-64 (2015).

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.

MSC:

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

Keywords:

polynomial wavelets; Chebyshev polynomials of second kind; orthogonality; Christoffel-Darboux formula; function approximation; wavelet series

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