Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem
arXiv:2005.10120 · doi:10.1007/s00023-022-01215-8
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.
49 pages, LaTeX, 2 figures, many small improvements, references added (published version)
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