Sampling approximation of smooth functions via generalized coiflets

We present the sampling approximation power of a newly constructed class of compactly supported orthonormal wavelets called generalized coiflets. We study the accuracy of generalized coiflets-based sampling approximation of smooth functions by developing convergence rates for the pointwise approximation error as well as its L^P-norm. We show: (i) that the L²-error due to the approximation of expansion coefficients by function samples is asymptotically negligible compared with that due to projection and (ii) that generalized coiflets can achieve asymptotically better approximation than the original coiflets