Localization of the generalized sampling series and its numerical application
Liwen Qian, Dennis B. Creamer · SIAM Journal on Numerical Analysis · 2006
We study the localization of the sampling series with general kernel and obtain its error estimates. To achieve exponentially decaying accuracy for the series to approximate a band-limited function and its derivatives, a sufficient condition is given and a rigorous criterion is provided for the sampling to obtain any desired accuracy. The result includes several known results as special cases and gives new results about wavelet sampling series.