Wavelet-Type Decompositions and Approximations from Shift-Invariant Spaces

We investigate sufficient conditions on principal shift-invariant spacesS(?) in order to provide prescribed approximation orders inLp(Rd), 1

[1]  Kang Zhao Simultaneous Approximation and Quasi-Interpolants , 1996 .

[2]  H. Triebel Theory Of Function Spaces , 1983 .

[3]  G. Kyriazis Approximation from shift-invariant spaces , 1995 .

[4]  C. D. Boor,et al.  Fourier analysis of the approximation power of principal shift-invariant spaces , 1992 .

[5]  R. Jia,et al.  Approximation by piecewise exponentials , 1991 .

[6]  C. Micchelli,et al.  On the approximation order from certain multivariate spline spaces , 1984, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[7]  Michael J. Johnson An upper bound on the approximation power of principal shift-invariant spaces , 1997 .

[8]  Charles A. Micchelli,et al.  Using the Refinement Equations for the Construction of Pre-Wavelets II: Powers of Two , 1991, Curves and Surfaces.

[9]  George C. Kyriazis,et al.  Approximation of Distribution Spaces by Means of Kernel Operators , 1995 .

[10]  I. J. Schoenberg Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions , 1988 .

[11]  Rong-Qing Jia,et al.  Controlled approximation and a characterization of the local approximation order , 1985 .

[12]  E. Cheney,et al.  Quasi-interpolation with translates of a function having noncompact support , 1992 .

[13]  Charles K. Chui,et al.  Cardinal Interpolation by Multivariate Splines , 1987 .

[14]  A. Ron Approximation Orders of and Approximation Maps from Local Principal Shift-Invariant Spaces , 1995 .

[15]  Approximation Orders of Principal Shift-Invariant Spaces Generated by Box Splines , 1996 .

[16]  R. DeVore,et al.  Approximation from Shift-Invariant Subspaces of L 2 (ℝ d ) , 1994 .