Sampling of operators

Details Sampling of operators Sampling of operators

2010-10-29

arxiv.org/abs/1010.6165v1

Mathematics

Functional Analysis

Scientific paper

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.

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