Wavelets based on orthogonal polynomials

被引：43

作者：

Fischer, B ^{[1
]}

Prestin, J ^{[1
]}

机构：

[1] UNIV ROSTOCK, FACHBEREICH MATH, D-18051 ROSTOCK, GERMANY

来源：

MATHEMATICS OF COMPUTATION | 1997年 / 66卷 / 220期

关键词：

orthogonal polynomials; polynomial wavelets; multiresolution analysis; kernel polynomials;

D O I：

10.1090/S0025-5718-97-00876-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a unified approach for the construction of polynomial wavelets. Our main tool is orthogonal polynomials. With the help of their properties we devise schemes for the construction of time localized polynomial bases on bounded and unbounded subsets of the real line. Several examples illustrate the new approach.

引用

页码：1593 / 1618

页数：26

共 10 条

[1]

Chihara TS., 1978, INTRO ORTHOGONAL POL

[2] ON TRIGONOMETRIC WAVELETS [J].

CHUI, CK ;

MHASKAR, HN .

CONSTRUCTIVE APPROXIMATION, 1993, 9 (2-3) :167-190

[3]

Davis P., 1963, Interpolation and Approximation

[4]

Fischer B, 1996, Tech. rep.

[5] BANACH ALGEBRAS FOR JACOBI SERIES AND POSITIVITY OF A KERNEL [J].

GASPER, G .

ANNALS OF MATHEMATICS, 1972, 95 (02) :261-&

[6] Polynomial wavelets on the interval [J].

Kilgore, T ;

Prestin, J .

CONSTRUCTIVE APPROXIMATION, 1996, 12 (01) :95-110

[7]

Plonka G., 1995, Advances in Computational Mathematics, V4, P357, DOI 10.1007/BF02123481

[8]

SZEGO G, 1959, AMS COLLOQUIM PUBLIC, V23

[9]

TASCHE M, 1995, NATO ADV SCI INST SE, V454, P497

[10]

TASCHE M, 1993, NUMER ALGORITHMS, V5, P453

← 1 →