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 equation.
- Pub Date:
- May 2020
- Mathematical Physics;
- Mathematics - Analysis of PDEs
- 49 pages, LaTeX, 2 figures, many small improvements, references added (published version)