Battle-Lemarie wavelet systems of natural orders are established in the paper. The main result work is decomposition theorem Besov and Triebel-Lizorkin spaces with local Muckenhoupt weights, which performed terms bases generated by such a type. wavelets splines suit very well for study integration operators.

Let φ be a compactly supported refinable function in L2(R) such that the shifts of φ are stable and φ̂(2ξ) = â(ξ)φ̂(ξ) for a 2π-periodic trigonometric polynomial â. A wavelet function ψ can be derived from φ by ψ̂(2ξ) := e−iξ â(ξ + π)φ̂(ξ). If φ is an orthogonal refinable function, then it is well known that ψ generates an orthonormal wavelet basis in L2(R). Recently, it has been shown in the liter...

This paper aims at studying the characterization of Dirac-structure edges with wavelet transform, and selecting the suitable wavelet functions to detect them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are presented: (1) slope invariant: the local maximum modulus of the wavelet transform of a Dirac-structure ...

Method for El Nino/Southern Oscillation: ENSO by means of wavelet based data compression with appropriate support length of base function is proposed. Through the experiments with observed southern oscillation index, the proposed method is validated. Also a method for determination of appropriate support length is proposed and is validated. KeywordsPrediction; Time series analysis; wavelet; ENS...

In identifying the spatial turbulent structure and its evolution in time, the wavelet autocorrelation analysis, which was proposed by author, was employed to analyze the velocity fluctuations in a plane turbulent jet at various positions with help of the complex wavelet function. The wavelet auto-correlation function can extract the most essential scales governing the self-similarity features o...

In linear approximation by wavelet, we approximate a given function by a finite term from the wavelet series. The approximation order is improved if the order of smoothness of the given function is improved, discussed by Cohen (2003), DeVore (1998), and Siddiqi (2004). But in the case of nonlinear approximation, the approximation order is improved quicker than that in linear case. In this study...