6 papers
Localized frames on Euclidean balls
Kevin Hughes, Arie Israel, Azita Mayeli
We construct explicit wave packet frames adapted to Euclidean balls and use them to obtain quantitative eigenvalue estimates for spatio--spectral limiting operators. Let \(d\geq 2\…
Trace bounds for limiting operators on rough domains
Kevin Hughes, Arie Israel, Azita Mayeli
This work concerns a quantitative form of Landau's eigenvalue theorem for spatio-spectral limiting operators. We isolate a simple mechanism that converts the problem of estimating…
First Steps towards Categorical Algebraic Artificial Chemistry
Joe Pratt-Johns, Toby St. Clere Smithe, Chris Guiver +2
We construct a functor that gives a dynamics to an algebraic model of interacting components. The construction generalises a computational model of Fontana and Buss in the field of…
Wave Packets and Eigenvalue Estimates for Limiting Operators on the Disk
Kevin Hughes, Arie Israel, Azita Mayeli
We study two-dimensional spatio-spectral limiting operators \[ T_R := P_{D(R)} B_S P_{D(R)} : L^2(\mathbb{R}^2) \rightarrow L^2(\mathbb{R}^2), \] where is a disk of radius $…
Wave packet systems and connections to spectral analysis of limiting operators
Kevin Hughes, Arie Israel, Azita Mayeli
We discuss the design of ``wave packet systems'' that admit strong concentration properties in phase space. We make a connection between this problem and topics in signal processin…
On the eigenvalue distribution of spatio-spectral limiting operators in higher dimensions, II
Kevin Hughes, Arie Israel, Azita Mayeli
Let , be bounded measurable sets in . Let be the orthogonal projection on the subspace of functions wi…