Orthonormal polynomial wavelets on the interval. (English) Zbl 1089.42022
Using a traditional orthonormal wavelet basis which is obtained by the integer translates and dilates of a mother wavelet, in section 2 the authors propose a general way of constructing a wavelet-like (with a similar multiresolution analysis structure) orthonormal basis in a separable Hilbert space. Applying this general method to the Chebyshev polynomials and Meyer wavelets, the authors obtain in section 3 an interesting polynomial wavelet-like orthonormal basis on the interval. The applications of these polynomial wavelet-like bases to the numerical resolution of degenerate elliptic operators are also addressed in section 4.
Reviewer: Bin Han (Edmonton)
MSC:
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
65T60 | Numerical methods for wavelets |
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