Partition of unity and density: A counterexample

Constructive Approximation

Volumn 13, Issue 2, 1997, Pages 251-260

  Jia, Rong Qing ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Density; Partition of unity; Shift invariant spaces; Splines

Indexed keywords

EID: 0031492786     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02678467     Document Type: Article

References (8)

1. C. DE BOOR, R. DEVORE (1985): Partitions of unity and approximation. Proc. Amer. Math. Soc., 93:705-709.
2. C. DE BOOR, R. DEVORE, K. HÖLLIG (1983): Approximation order from smooth pp functions. In: Approximation Theory IV (C. K. Chui, L. L. Schumaker, J. Ward, eds.). New York: Academic Press, pp. 353-357.
3. L. EHRENPREIS (1970): Fourier Analysis in Several Complex Variables. Tracts in Mathematics, vol. 17. New York: Wiley-Interscience.
4. R.-Q. JIA (1991): A characterization of the approximation order of translation invariant spaces. Proc. Amer. Math. Soc., 111:61-70.
5. R.-Q. JIA (1995): The Toeplitz theorem and its applications to approximation theory and linear PDEs. Trans. Amer. Math. Soc., 347:2585-2594.
6. R.-Q. JIA (to appear): Shift-invariant spaces on the real line. Proc. Amer. Math. Soc.
7. R.-Q. JIA, S. D. RIEMENSCHNEIDER, Z. W. SHEN (1994): Solvability of systems of linear operator equations. Proc. Amer. Math. Soc., 120:815-824.
8. A. RON (1991): A characterization of the approximation order of multivariate spline spaces. Studia Math., 98:73-90.