2024/03/19 by Kevin Hughes, Hughes, Kevin, Arie Israel +3 · 2 citations
Computer Science · Mathematics · #42B10 #47A75 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2403.13092
openalex publication_date 2024/03/19 · openalex created_date 2024/03/22 · openalex updated_date 2026/07/28
Let F, S be bounded measurable sets in ℝd. Let PF : L2(ℝd) → L2(ℝd) be the orthogonal projection on the subspace of functions with compact support on F, and let BS : L2(ℝd) → L2(ℝd) be the orthogonal projection on the subspace of functions with Fourier transforms having compact support on S. In this paper, we derive improved distributional estimates on the eigenvalue sequence 1 ≥ λ1(F,S) ≥ λ2(F,S) ≥ ⋯ > 0 of the spatio-spectral limiting operator BS PF BS : L2(ℝd) → L2(ℝd). The significance of such estimates lies in their diverse applications in medical imaging, signal processing, geophysics and astronomy. Our proof is based on the decomposition techniques developed in \citeMaRoSp23. The novelty of our approach is in the use of a two-stage dyadic decomposition with respect to both the spatial and frequency domains, and the application of the results in \citeArieAzita23 on the eigenvalues of spatio-spectral limiting operators associated to cubical domains.