Optimal Holder-Zygmund exponent of semi-regular refinable functions

JOURNAL OF APPROXIMATION THEORY

卷:251

Article

Charina, Maria¹  Conti, Costanza²  Romani, Lucia³  Stoeckler, Joachim⁴  Viscardi, Alberto³ 

[1] Univ Wien, Fak Math, Vienna, Austria

[2] Univ Firenze, Dipartimento Ingn Ind, Florence, Italy

[3] Alma Mater Studiorum Univ Bologna, Dipartimento Matemat, Bologna, Italy

[4] TU Dortmund, Inst Angew Math, Dortmund, Germany

关键词: Wavelet tight frames;    Semi-regular refinement;    Dubuc-Deslauriers frames;    Holder-Zygmund regularity;   

DOI  :  10.1016/j.jat.2019.105340

来源: Elsevier

【 摘 要 】

The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting is crucial for these approaches. We propose an efficient method based on wavelet tight frame decomposition techniques for estimating Holder-Zygmund regularity of univariate semi-regular refinable functions generated, e.g., by subdivision schemes defined on semi-regular meshes t = -h(l)N boolean OR {0} boolean OR h(r)N, h(l), h(r) is an element of (0, infinity). To ensure the optimality of this method, we provide a new characterization of Helder-Zygmund spaces based on suitable irregular wavelet tight frames. Furthermore, we present proper tools for computing the corresponding frame coefficients in the semi-regular setting. We also propose a new numerical approach for estimating the optimal Holder-Zygmund exponent of refinable functions which is more efficient than the linear regression method. We illustrate our results with several examples of known and new semi-regular subdivision schemes with a potential use in blending curve design. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free