Sobolev Exponent Estimate and Asymptotic Regularity of M Band Daubechies' Scaling Functions
نویسنده
چکیده
In this paper, direct estimate of Sobolev exponent of reenable distributions and its application to the asymptotic estimate of Sobolev exponent of M band Daubechies' scaling functions are considered.
منابع مشابه
Asymptotic Regularity of Daubechies’ Scaling Functions
Let φN , N ≥ 1, be Daubechies’ scaling function with symbol ( 1+e−iξ 2 )N QN (ξ), and let sp(φN ), 0 < p ≤ ∞, be the corresponding Lp Sobolev exponent. In this paper, we make a sharp estimation of sp(φN ), and we prove that there exists a constant C independent of N such that N − ln |QN (2π/3)| ln 2 − C N ≤ sp(φN ) ≤ N − ln |QN (2π/3)| ln 2 . This answers a question of Cohen and Daubeschies (Re...
متن کاملWavelets with Optimal Sobolev Regularity
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments. The increased regularity is obtained by optimizing the locations of the roots the scaling filter has on the interval (π/2, π). The results improve those obtai...
متن کاملOrthonormal Compactly Supported Wavelets with Optimal Sobolev Regularity
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments. The increased regularity is obtained by optimizing the locations of the roots the scaling filter has on the interval (π/2, π). The results improve those obtai...
متن کاملAsymptotic Behaviour of M-Band Scaling Functions of Daubechies Type
In this paper, we consider the asymptotic behaviour of M-band scaling functions of Daubechies type as M tends to innnity.
متن کاملSobolev exponents of Butterworth refinable functions
The precise Sobolev exponent s∞(φn) of the Butterworth refinable function φn associated with the Butterworth filter of order n, bn(ξ) := cos2n(ξ/2) cos2n(ξ/2)+sin2n(ξ/2) , is shown to be s∞(φn) = n log2 3+ log2(1+ 3−n). This recovers the previously given asymptotic estimate of s∞(φn) of Fan and Sun [1], and gives more accurate regularity of Butterworth refinable function φn. AMS 2000 Subject Cl...
متن کامل