Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem
Mathematical Physics
2023-02-16 v2 Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.2005.10120,
title = {Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem},
author = {Felix Finster and Claudio F. Paganini},
journal= {arXiv preprint arXiv:2005.10120},
year = {2023}
}
Comments
49 pages, LaTeX, 2 figures, many small improvements, references added (published version)