Sampling of operators
Functional Analysis
2010-11-01 v1 Information Theory
Classical Analysis and ODEs
math.IT
Abstract
Sampling and reconstruction of functions is a central tool in science. A key result is given by the sampling theorem for bandlimited functions attributed to Whittaker, Shannon, Nyquist, and Kotelnikov. We develop an analogous sampling theory for operators which we call bandlimited if their Kohn-Nirenberg symbols are bandlimited. We prove sampling theorems for such operators and show that they are extensions of the classical sampling theorem.
Cite
@article{arxiv.1010.6165,
title = {Sampling of operators},
author = {Götz E. Pfander},
journal= {arXiv preprint arXiv:1010.6165},
year = {2010}
}