A NOTE ON ORTHONORMAL POLYNOMIAL BASES AND WAVELETS

被引：27

作者：

OFFIN, D ^{[1
]}

OSKOLKOV, K ^{[1
]}

机构：

[1] QUEENS UNIV,DEPT MATH & STAT,KINGSTON K7L 3N6,ONTARIO,CANADA

来源：

CONSTRUCTIVE APPROXIMATION | 1993年 / 9卷 / 2-3期

关键词：

ORTHONORMAL TRIGONOMETRIC POLYNOMIAL BASES; WAVELETS; PROJECTIONS; BEST APPROXIMATION;

D O I：

10.1007/BF01198009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A simple and explicit construction of an orthonormal trigonometric polynomial basis in the space C of continuous periodic functions is presented. It consists simply of periodizing a well-known wavelet on the real line which is orthonormal and has compactly supported Fourier transform. Trigonometric polynomials resulting from this approach have optimal order of growth of their degrees if their indices are powers of 2. Also, Fourier sums with respect to this polynomial basis are projectors onto subspaces of trigonometric polynomials of high degree, which implies almost best approximation properties.

引用

页码：319 / 325

页数：7