Perturbations of the Haar wavelet

Let m is an element of Z(+) be given. For any epsilon > 0 we construct a function f({epsilon}) having the following properties: (a) f({epsilon}) has support in [-epsilon, 1 + epsilon]. (b) f({epsilon}) is an element of C-m(-infinity, infinity). (c) If h denotes the Haar function and 0 < delta < infinity, then \\f({epsilon})-h\\(L delta(R)) less than or equal to (1 + 2(delta))(1/delta)(2 epsilon)(1/delta). (d) f({epsilon}) generates an affine Riesz basis whose frame bounds (which are given explicitly) converge to 1 as epsilon --> 0.