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Local Sampling and Approximation of Operators with Bandlimited Kohn--Nirenberg Symbols


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Krahmer, Felix ; Pfander, Götz E.:
Local Sampling and Approximation of Operators with Bandlimited Kohn--Nirenberg Symbols.
In: Constructive approximation. 39 (Juni 2014) 3. - S. 541-572.
ISSN 0176-4276 ; 1432-0940


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Recent sampling theorems allow for the recovery of operators with bandlimited Kohn--Nirenberg symbols from their response to a single discretely supported identifier signal. The available results are inherently nonlocal. For example, we show that in order to recover a bandlimited operator precisely, the identifier cannot decay in time or in frequency. Moreover, a concept of local and discrete representation is missing from the theory. In this paper, we develop tools that address these shortcomings. We show that to obtain a local approximation of an operator, it is sufficient to test the operator on a truncated and mollified delta train, that is, on a compactly supported Schwarz class function. To compute the operator numerically, discrete measurements can be obtained from the response function which is localized in the sense that a local selection of the values yields a local approximation of the operator. Central to our analysis is the conceptualization of the meaning of localization for operators with bandlimited Kohn--Nirenberg symbols.

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Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen
Open Access: Freie Zugänglichkeit des Volltexts?:Nein
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Titel an der KU entstanden:Nein
Eingestellt am: 17. Aug 2017 08:32
Letzte Änderung: 12. Feb 2020 11:02
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