Bivariate constrained wavelet approximation


Shape-preserving properties of some naturally arising bivariate wavelet operators Bn are examined. Namely, let f∈Ck(R2), k > 0, r, s≥ 0, all integers such that r + s = k. If ∂ r+s{cauchy integral} (∂ xr∂ ys)(x,y)≥ 0, then it is proved, under mild conditions of Bn, that ∂ r+s (∂ xr∂ ys)Bn({cauchy integral})(x,y)≥ 0; also pointwise converge of Bn({cauchy integral}) to {cauchy integral} is given with rates through a Jackson-type inequality. Associated simultaneous shape-preserving results are also presented for special type of wavelet operators Bn. © 1994.

Publication Title

Journal of Computational and Applied Mathematics