On stability and orthogonality of refinable functions

被引：1
|
作者：
Saliani, Sandra [1 ]
机构：
[1] Univ Basilicata, Dipartimento Matemat, I-85100 Potenza, Italy
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2006年 / 21卷 / 02期
关键词：
wavelet; refinable function; Riesz basis; low-pass filter;
D O I：
10.1016/j.acha.2006.01.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give a simple proof of Lawton's theorem on the orthogonality of translates of a compactly supported refinable function. The same technique provides an easy proof of uniqueness in Gundy's criterion on the characterization of low-pass filters associated to prescaling functions. (C) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：254 / 261
页数：8
相关论文
共 50 条
  • [41] Causality properties of refinable functions and sequences
    Say Song Goh
    Tim N. T. Goodman
    S. L. Lee
    Advances in Computational Mathematics, 2007, 26 : 231 - 250
  • [42] Neural Network Approximation of Refinable Functions
    Daubechies, Ingrid
    De Vore, Ronald
    Dym, Nadav
    Faigenbaum-Golovin, Shira
    Kovalsky, Shahar Z.
    Lin, Kung-Chin
    Park, Josiah
    Petrova, Guergana
    Sober, Barak
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2023, 69 (01) : 482 - 495
  • [43] On the volume of sets bounded by refinable functions
    Hakenberg, Jan
    Reif, Ulrich
    APPLIED MATHEMATICS AND COMPUTATION, 2016, 272 : 2 - 19
  • [44] A class of orthogonal refinable functions and wavelets
    Goodman, TNT
    CONSTRUCTIVE APPROXIMATION, 2003, 19 (04) : 525 - 540
  • [45] Refinable spline functions and Hermite interpolation
    Goodman, TNT
    MATHEMATICAL METHODS FOR CURVES AND SURFACES: OSLO 2000, 2001, : 147 - 161
  • [46] Differentiability of multivariate refinable functions and factorization
    Thomas Sauer
    Advances in Computational Mathematics, 2006, 25 : 211 - 235
  • [47] Sobolev exponents of Butterworth refinable functions
    Kim, Hong Oh
    Kim, Rae Young
    APPLIED MATHEMATICS LETTERS, 2008, 21 (05) : 510 - 515
  • [48] A Class of Orthogonal Refinable Functions and Wavelets
    Tim N.T. Goodman
    Constructive Approximation, 2003, 19 : 525 - 540
  • [49] Gauss quadrature for refinable weight functions
    Gautschi, W
    Gori, L
    Pitolli, F
    APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2000, 8 (03) : 249 - 257
  • [50] Differentiability of multivariate refinable functions and factorization
    Sauer, Thomas
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2006, 25 (1-3) : 211 - 235
12345