Band-limited functions: $L\sp p$-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...

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 ...

Frames and Oversampling Formulas for Band Limited Functions

In this article we obtain families of frames for the space Bω of functions with band in [−ø, ø] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant, due to Bownik, of their characterization of families of functions whose shifts form frames or Riesz bases. We give necessary and sufficient conditions for the translates o...