Quasi-interpolation in shift invariant spaces

[摘要] Let s greater than or equal to 1 be an integer, phi : R-s --> R be a compactly supported function, and S(phi) denote the linear span of {phi>(*) over bar *(.- k) : k epsilon Z(s)}. We consider the problem of approximating a continuous function f: R-s --> R on compact subsets of R-s from the classes S(phi>(*) over bar * (h.)), h > 0, based on samples of the function at scattered sites in R-s. We demonstrate how classical polynomial inequalities lead to the construction of local, quasi-interpolatory operators for this purpose, (C) 2000 Academic Press.

[发布日期] 2000-11-01