Shift-invariant spaces on the real line

被引：43

作者：

Jia, RQ

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1997年 / 125卷 / 03期

关键词：

shift-invariant spaces; approximation order;

D O I：

10.1090/S0002-9939-97-03586-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in L(p)(R) (1 less than or equal to p less than or equal to infinity). Based on a study of linear independence of the shifts of the;generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on Z. Moreover, we show that such a shift;invariant space provides L(p)-approximation order k if and only if it contains all polynomials of degree less than k.

引用

收藏

页码：785 / 793

页数：9

相关论文

共 19 条

[1] ON THE INTEGER TRANSLATES OF A COMPACTLY SUPPORTED FUNCTION - DUAL BASES AND LINEAR PROJECTORS [J].

BENARTZI, A ;

RON, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1990, 21 (06) :1550-1562

[2] PARTITIONS OF UNITY AND APPROXIMATION [J].

DEBOOR, C ;

DEVORE, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 93 (04) :705-709

[3] APPROXIMATION FROM SHIFT-INVARIANT SUBSPACES OF L(2(R(D)) [J].

DEBOOR, C ;

DEVORE, RA ;

RON, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 341 (02) :787-806

[4] THE STRUCTURE OF FINITELY GENERATED SHIFT-INVARIANT SPACES IN L(2)(R(D)) [J].

DEBOOR, C ;

DEVORE, RA ;

RON, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 119 (01) :37-78

[5] APPROXIMATION ORDER FROM BIVARIATE C1-CUBICS - A COUNTEREXAMPLE [J].

DEBOOR, C ;

HOLLIG, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 87 (04) :649-655

[6] A SHARP UPPER BOUND ON THE APPROXIMATION ORDER OF SMOOTH BIVARIATE PP FUNCTIONS [J].

DEBOOR, C ;

JIA, RQ .

JOURNAL OF APPROXIMATION THEORY, 1993, 72 (01) :24-33

[7] THE TOEPLITZ THEOREM AND ITS APPLICATIONS TO APPROXIMATION-THEORY AND LINEAR PDES [J].

JIA, RQ .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (07) :2585-2594

[8] A CHARACTERIZATION OF THE APPROXIMATION ORDER OF TRANSLATION INVARIANT SPACES OF FUNCTIONS [J].

JIA, RQ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 111 (01) :61-70

[9] APPROXIMATION BY MULTIINTEGER TRANSLATES OF FUNCTIONS HAVING GLOBAL SUPPORT [J].

JIA, RQ ;

LEI, JJ .

JOURNAL OF APPROXIMATION THEORY, 1993, 72 (01) :2-23

[10]

JIA RQ, 1992, IN PRESS P EDINBURGH, V36, P69