BIVARIATE CONSTRAINED WAVELET APPROXIMATION

Shape-preserving properties of some naturally arising bivariate wavelet operators B-n are examined. Namely, let f is an element of C-k(R(2)), k > 0, r, s greater than or equal to 0, all integers such that r + s = k. If partial derivative(r+s)f/(partial derivative x(r) partial derivative y(s))(x, y)greater than or equal to 0, then it is proved, under mild conditions on B-n, that partial derivative(r+s)/(partial derivative x(r) partial derivative y(s))B-n(f)(x, y)greater than or equal to 0; also pointwise converge of B-n(f) to f is given with rates through a Jackson-type inequality. Associated simultaneous shape-preserving results are also presented for special type of wavelet operators B-n.