Compactly supported symmetric \(C^\infty\) wavelets with spectral approximation order. (English) Zbl 1161.42312
Summary: We obtain symmetric \(C^\infty\) real-valued tight wavelet frames in \(L_2(\mathbb{R})\) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported \(C^\infty\) orthonormal complex wavelets in \(L_2(\mathbb{R})\). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in \(L_2(\mathbb{R})\) is given.
MSC:
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
41A25 | Rate of convergence, degree of approximation |
41A05 | Interpolation in approximation theory |
42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |