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Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt’s Theorem

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Finster, Felix ; Paganini, Claudio F.
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Date of publication of this fulltext: 20 Sep 2022 05:36

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We prove quantitative versions of the following statement: If a solution of the 1+1-dimensional wave equation has spatially compact support and consists mainly of positive frequencies, then it must have a significant high-frequency component. Similar results are proven for the 3+1-dimensional wave equation.

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