C2 interpolation with range restriction

Given-8 < ? < ? < 8, E C R-n finite, and f : E -[?, ?], how can we extend f to a C-m(R-n) function F such that ? = F=A and IIF IIC m(R-n) is within a constant multiple of the least possible, with the constant depending only on m and n? In this paper, we provide the solution to the problem for the case m = 2. Specifi-cally, we construct a (parameter-dependent, nonlinear) C-2(R-n) extension operator that preserves the range [A, A], and we provide an efficient algorithm to compute such an extension using O(N log N) operations, where N = #(E).