Approximation Orders of and Approximation Maps from Local Principal Shift-Invariant Spaces

摘要

Approximation orders of shift-invariant subspaces of Lp(Rd), p is between 2 andinfinity, generated by the shifts of one compactly supported function are considered. In that course, explicit approximation maps are constructed. The approach avoids quasi-interpolation and applies to stationary and non-stationary refinements. The general results are specialized to box spline spaces, to obtain new results on their approximation orders.