Shift-invariant spaces on the real line

Proceedings of the American Mathematical Society

Volumn 125, Issue 3, 1997, Pages 785-793

  Jia, Rong Qing ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Approximation order; Shift invariant spaces

Indexed keywords

EID: 21744439767     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03586-7     Document Type: Article

References (18)

1. A. Ben-Artzi and A. Ron, On the integer translates of a compactly supported function: dual bases and linear projectors, SIAM J. Math. Anal. 21 (1990), 1550-1562. MR 91j:41009
2. C. de Boor and R. DeVore, Partitions of unity and approximation, Proc. Amer. Math. Soc. 93 (1985), 705-709. MR 86f:41003
3. d), Trans. Amer. Math. Soc. 341 (1994), 787-806. MR 94d:41028
4. d), J- Functional Analysis 119 (1994), 37-78. MR 95g:46050
5. 1-cubics: a counterexample, Proc. Amer. Math. Soc. 87 (1983), 649-655. MR 84j:41014
6. C. de Boor and R. Q. Jia, A sharp upper bound on the approximation order of smooth bivariate pp functions, J. Approx. Theory 72 (1993), 24-33. MR 94e:41012
7. R. Q. Jia, A characterization of the approximation order of translation invariant spaces, Proc. Amer. Math. Soc. Ill (1991), 61-70. MR 91d:41018
8. _, The Toeplitz theorem and its applications to approximation theory and linear PDE's, Trans. Amer. Math. Soc. 347 (1995), 2585-2594. CMP 94:13
9. R. Q. Jia and J. J. Lei, Approximation by multiinteger translates of functions having global support, 3. Approx. Theory 72 (1993), 2-23. MR 94f:41024
10. R. Q. Jia and C. A. Micchelli, On linear independence of integer translates of a finite number of functions, Research Report CS-90-10 (1990), University of Waterloo. A revised version appeared in Proc. Edinburgh Math. Soc. 36 (1992), 69-85. MR 94e:41044
11. _, Using the refinement equation for the construction of pre-wavelets II: Powers of two, Curves and Surfaces (P. J. Laurent, A. Le Méhauté, and L. L. Schumaker, eds.), Academic Press, New York, 1991, pp. 209-246. MR 92c:65006
12. A. Ron, Factorization theorem for univariate splines on regular grids, Israel J. Math. 70 (1990), 48-68. MR 91g:65025
13. _, A characterization of the approximation order of multivariate spline spaces, Studia Math. 98 (1991), 73-90. MR 92g:41017
14. M. Schechter, Principles of Functional Analysis, Academic Press, New York, 1971. MR 56:3607
15. I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math. 4 (1946), 45-99, 112-141. MR 8:55d
16. G. Strang and G. Fix, A Fourier analysis of the finite-element variational method, Constructive Aspects of Functional Analysis (G. Geymonat, ed.), C.I.M.E. (1973), 793-840.
17. K. Zhao, Global linear independence and finitely supported dual basis, SIAM J. Math. Anal. 23 (1992), 1352-1355. MR 93h:41034
18. _, Approximation from locally finite-dimensional shift-invariant spaces, Proc. Amer. Math. Soc. 124 (1996), 1857-1867. MR 96h:41019