Order of linear approximation from shift-invariant spaces

被引：41
作者：
Jetter, K
Zhou, DX
机构：
[1] Fachbereich Mathematik, Universität Duisburg, Duisburg
来源：
CONSTRUCTIVE APPROXIMATION | 1995年 / 11卷 / 04期
关键词：
approximation order; Fourier transform; quasi-interpolation; cardinal interpolation; shift-invariant space;
D O I：
10.1007/BF01208430
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Fourier analysis approach is taken to investigate the approximation order of scaled versions of certain linear operators into shift-invariant subspaces of L(2)(R(d)), Quasi-interpolants and cardinal interpolants are special operators of this type, and we give a complete characterization of the order in terms of some type of ellipticity condition for a related function. We apply these results by showing that the L(2)-approximation order of a closed shift-invariant subspace can often he realized by such an operator.
引用
收藏
页码：423 / 438
页数：16
相关论文
共 18 条
  • [1] Buhmann M.D., 1993, MULTIVARIATE APPROXI, P35
  • [2] BURCHARD HG, 1993, COORDINATE ORDER APP
  • [3] Chui C.K, 1988, MULTIVARIATE SPLINES, V54
  • [4] CARDINAL INTERPOLATION WITH DIFFERENCES OF TEMPERED FUNCTIONS
    CHUI, CK
    WARD, JD
    JETTER, K
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1992, 24 (12) : 35 - 48
  • [5] CHUI CK, 1987, MATH COMPUT, V48, P711, DOI 10.1090/S0025-5718-1987-0878701-2
  • [6] de Boor C., 1993, BOX SPLINES
  • [7] DEBOOR C, 1990, NATO ADV SCI I C-MAT, V307, P313
  • [8] APPROXIMATION FROM SHIFT-INVARIANT SUBSPACES OF L(2(R(D))
    DEBOOR, C
    DEVORE, RA
    RON, A
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 341 (02) : 787 - 806
  • [9] FOURIER-ANALYSIS OF THE APPROXIMATION POWER OF PRINCIPAL SHIFT-INVARIANT SPACES
    DEBOOR, C
    RON, A
    [J]. CONSTRUCTIVE APPROXIMATION, 1992, 8 (04) : 427 - 462
  • [10] DEBOOR C, 1993, APPROXIMATION THEORY, V7, P1
12