A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice Γ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice Γ ∗ as lattice of periods. This state...

Abstract Inspired by Jaming’s characterization of the Fourier transform on specific groups via convolution property, we provide a novel approach which characterizes any locally compact abelian group. In particular, our encompasses results. Furthermore, demonstrate that cosine as well Laplace can also be characterized suitable property.

Inspired by an extension of Wiener's lemma on the relation measures μ unit circle and their Fourier coefficients μˆ(kn) along subsequences (kn) natural numbers Cuny, Eisner Farkas [1], we study validity when are weighted a sequence probability measures. By using convergence with respect to filter derived from these measure sequences, obtain similar results, now also allowing consideration local...