Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.10120
- arXiv:
- arXiv:2005.10120
- Bibcode:
- 2020arXiv200510120F
- Keywords:
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- Mathematical Physics;
- Mathematics - Analysis of PDEs
- E-Print:
- 49 pages, LaTeX, 2 figures, many small improvements, references added (published version)