Almost periodic generalized ultradistributions

Sampling and Generalized Almost Periodic Extension of Functions

This brief explores the connections between nonuniform sampling of a certain function and the almost periodic extension of its Fourier transform. It is shown that the Fourier transform of a band-limited function can be extended (as a weighted sum of translates) as a Stepanoff almost periodic function to the whole frequency axis. This result leads to a generalized nonuniform sampling theorem whi...

Generalized Fourier-Bessel operator and almost-periodic interpolation and approximation

We consider functions f of two real variables, given as trigonometric functions over a finite set F of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle 2kπ M for some integer M . Firstly, we address the problem of evaluating these functions over a similar finite set E in the space plane and, secondly, we address the problems of interpolating or appro...

Characterization of almost maximally almost-periodic groups

Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...

Almost Periodic Harmonizable Processes

The class of harmonizable processes is a natural extension of the class of stationary processes. This paper provides sufficient conditions for the sample paths of harmonizable processes to be almost periodic uniformly, Stepanov and Besicovitch.

Almost Periodic Compactifications