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Sampling of operators

2010/10/29 by Götz E. Pfander, Pfander, Götz E.
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #advanced mathematical theories #cs.IT #math.CA #math.FA #math.IT #msc:35S05 #msc:42B35 #msc:47B35 #msc:94A20

paper · pdf · doi:10.48550/arxiv.1010.6165

arxiv created 2010/10/29 · arxiv updated 2010/11/01

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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