APPROXIMATION FROM SHIFT-INVARIANT SUBSPACES OF L(2(R(D))

被引：245

作者：

DEBOOR, C ^{[1
]}

DEVORE, RA ^{[1
]}

RON, A ^{[1
]}

机构：

[1] UNIV S CAROLINA,DEPT MATH,COLUMBIA,SC 29208

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 341卷 / 02期

关键词：

APPROXIMATION ORDER; STRANG-FIX CONDITIONS; SHIFT-INVARIANT SPACES; RADIAL BASIS FUNCTIONS; ORTHOGONAL PROJECTION;

D O I：

10.2307/2154583

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A complete characterization is given of closed shift-invariant subspaces of L2(R(d)) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to decay at infinity. The approximation order of a general closed shift-invariant space is shown to be already realized by a specifiable principal subspace.

引用

页码：787 / 806

页数：20

共 37 条

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