Sampling of operators
G\"otz E. Pfander

TL;DR
This paper extends classical sampling theory to operators by developing a sampling theorem for bandlimited operators, based on their Kohn-Nirenberg symbols, generalizing the concept from functions to operators.
Contribution
It introduces a novel sampling theorem for bandlimited operators, extending classical function sampling results to the operator setting using Kohn-Nirenberg symbols.
Findings
Sampling theorems for bandlimited operators are established.
Operators with bandlimited Kohn-Nirenberg symbols can be reconstructed from samples.
The results generalize classical sampling theorems for functions.
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.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · advanced mathematical theories · Advanced Harmonic Analysis Research
