Year: 2025
Type: preprint
Abstract: We present a sufficient condition on sets $E$ and $F$ in $\mathbb{R}^d$ to ensure compactness of Fourier concentration operators by introducing the notion of sets which are very thin at infinity. We are able to show that if the sets $E$ and $F$ are both very thin at infinity, then the associated Fourier concentration operator is compact on $L^2(\mathbb{R}^d)$. The proof relies on a combination of the Logvinenko-Sereda uncertainty principle together with an uncertainty principle due to Shubin, Vakilian and Wolff. This provides a partial answer to a question posed by Katsnelson and Machluf on truncated Fourier operators.
Source: arXiv (Cornell University)
Author: Samuelsen, Helge J{\o}rgen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979325284
Cites:
Cited by:
Related to: