Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces
نویسندگان
چکیده
We investigate the construction of all reproducing kernel Hilbert spaces of functions on a domain Ω ⊂ R that have a countable sampling set Λ ⊂ Ω. We also characterize all the reproducing kernel Hilbert spaces that have a prescribed sampling set. Similar problems are considered for reproducing kernel Banach spaces, but now with respect to Λ as a 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. The results of this paper uncover precisely the affinity between stable sampling expansions and reproducing kernel Hilbert and Banach spaces. 2000 Mathematics Subject Classification. Primary 94A20, 42C15, 46C05, 47B10.
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