Given an arbitrary finite set of data F = {f1, ..., fm} ⊂ L2(Rd) we prove the existence and show how to construct a “small shift invariant space” that is “closest” to the data F over certain class of closed subspaces of ...

We prove the existence of Riesz bases of exponentials of L2(Ω), provided that Ω ⊂ ℝd is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic ...

We study the zero sets of random analytic functions generated by a sum of the cardinal sine functions which form an orthonormal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian ...

The classical results on oversampling and undersampling (or aliasing) of functions in Paley–Wiener spaces are generalized to the case of functions in de Branges spaces arising from regular Schrödinger operators with a wide ...

We prove the existence of sampling sets and interpolation sets near the critical density, in Paley Wiener spaces of a locally compact abelian (LCA) group G. This solves a problem left by Gröchenig, Kutyniok, and Seip in ...

The class of global Gevrey functions was introduced recently by Z. Adwan, G. Hoepfner and A. Raich, the elements in these spaces are defined in terms of its derivatives with estimates that depend on sequences. It is know ...

We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated ...