Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces
Given a countable subset of a set , we investigate the construction of all the reproducing kernel Hilbert (resp. Banach) spaces on that have as a sampling (resp. p-sampling) set. Unlike the general p-frames, we prove that every p-sampling set for a reproducing kernel Banach space yields a reconstruction formula. Some applications are given to demonstrate the general construction.
Numerical Functional Analysis and Optimization
"Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces" (2009). Faculty Bibliography 2000s. 1619.