Band-limited functions: $L^p $-convergence

Band-limited Functions: / / -convergence

Relevant Sampling of Band-limited Functions

We study the random sampling of band-limited functions of several variables. If a band-limited function with bandwidth has its essential support on a cube of volume R, then O(Rd logR) random samples suffice to approximate the function up to a given error with high probability.

Band Limited Functions on Quantum Graphs

The notion of band limited functions is introduced on a quantum graph. The main results of the paper are a uniqueness theorem and a reconstruction algorithm of such functions from discrete sets of values. It turns out that some of our band limited functions can have compact supports and their frequencies can be localized on the “time” side. It opens an opportunity to consider signals of a varia...

Orthonormal Basis Functions for Continuous-Time Systems and Lp Convergence

In this paper, model sets for continuous–time linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and two–parameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space H1(Π) under the same condition as previously derived by the authors for the norm denseness in the (Π ...

One-sided Band-limited Approximations of Some Radial Functions

We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically extremal as the sides of the box become uniformly large. We then adapt the Distribution and Gaussian Subordination methods of [12] to the multidimensional setting ...