Perron-Frobenius operators and the Klein-Gordon equation
Francisco Canto-Martin, Haakan Hedenmalm, Alfonso Montes-Rodriguez
TL;DR
This paper investigates the non-uniqueness of solutions to the Klein-Gordon equation in one dimension, focusing on the structure of solution spaces when solutions vanish on certain sets, revealing infinite-dimensional solution spaces in specific cases.
Contribution
It characterizes the non-uniqueness sets for Klein-Gordon solutions with finite measure Fourier transforms, especially for lattice-crosses, and shows the solution space can be infinite-dimensional.
Findings
Non-uniqueness sets are characterized for solutions with finite measure Fourier transforms.
For lattice-crosses, the solution space vanishing there is infinite-dimensional.
The study links the structure of solutions to properties of Perron-Frobenius operators.
Abstract
We study the non-uniqueness sets for solutions to the Klein-Gordon equation in 1 space dimension, for solutions whose Fourier transform is a finite complex measure absolutely continuous with respect to arc length. We show that generally, in the non-unique case for lattice-crosses, the space of solutions that vanish there is infinite-dimensional.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.