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• W2012616405 abstract "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." @default.
• W2012616405 created "2016-06-24" @default.
• W2012616405 creator A5011675506 @default.
• W2012616405 creator A5090264479 @default.
• W2012616405 date "2014-04-22" @default.
• W2012616405 modified "2023-09-30" @default.
• W2012616405 title "Local Sampling and Approximation of Operators with Bandlimited Kohn–Nirenberg Symbols" @default.
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• W2012616405 doi "https://doi.org/10.1007/s00365-014-9228-4" @default.
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