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+1dimensional wave equation has spatially compact support and consists mainly of positive frequencies, then it must have a significant highfrequency component. Similar results are proven for the 3+1dimensional wave equation.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.10120
 arXiv:
 arXiv:2005.10120
 Bibcode:
 2020arXiv200510120F
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 49 pages, LaTeX, 2 figures, many small improvements, references added (published version)