Band limited functions on quantum graphs

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...

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.

On the Extrapolation of Band-Limited Functions with Energy Constraints

Abstruct-A modification of the algorithm proposed by Papoulis and Gerchberg for extrapolating band-limited functions’ is suggested to extend its applicability over data corrupted by noise. We assume that energy constraints are known either for the band-limited signal or for the noise. In addition, the discrete formulation of the iterative algorithm is derived, and the transition from the con...

Irregular sampling of band-limited functions on the sphere

Article history: Received 27 September 2013 Received in revised form 5 May 2014 Accepted 13 May 2014 Available online xxxx Communicated by W.R. Madych MSC: 65T99 42C10 33C55 65D15