WAVELETS OF MULTIPLICITY-R

被引：198

作者：

GOODMAN, TNT ^{[1
]}

LEE, SL ^{[1
]}

机构：

[1] NATL UNIV SINGAPORE,DEPT MATH,SINGAPORE 0511,SINGAPORE

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 342卷 / 01期

关键词：

WAVELETS; MULTIPLICITY; DECOMPOSITION AND RECONSTRUCTION ALGORITHMS; DUALITY PRINCIPLE; RIESZ BASIS; CARDINAL SPLINES WITH MULTIPLE KNOTS;

D O I：

10.2307/2154695

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A multiresolution approximation (V(m))m is-an-element-of Z of L2(R) is of multiplicity r > 0 if there are r functions phi1, ... , phi(r) whose translates form a Riesz basis for V0. In the general theory we derive necessary and sufficient conditions for the translates of phi1, ... , phi(r), psi1, ... , psi(r) to form a Riesz basis for V1. The resulting reconstruction and decomposition sequences lead to the construction of dual bases for V0 and its orthogonal complement W0 in V1. The general theory is applied in the construction of spline wavelets with multiple knots. Algorithms for the construction of these wavelets for some special cases are given.

引用

页码：307 / 324

页数：18

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