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

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

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 e...

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Veröffentlicht in:arXiv.org 2022-06
Hauptverfasser: Finster, Felix, Paganini, Claudio F
Format: Artikel
Sprache:eng
Schlagworte:
Incompatibility
Mathematics - Analysis of PDEs
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Quantitative analysis
Wave equations
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Beschreibung
Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2005.10120