Multivariate probabilistic approximation in wavelet structure


Let {Mathematical expression} and F(x,y) be a continuous distribution function on R2. Then there exist linear wavelet operators Ln(F,x,y) which are also distribution function and where the defining them mother wavelet is φ0(x,y). These approximate F(x,y) in the supnorm. The degree of this approximation is estimated by establishing a Jackson type inequality. Furthermore we give generalizations for the case of a mother wavelet φ0, which is just any distribution function on R2 also we extend these results in R2,r>2 © 1992 Springer.

Publication Title

Approximation Theory and its Applications