It is the purpose of this paper to feature the link between the theory of minimal norm interpolation over lattices by elements from Sobolev algebras Hs(R) with what is known as the theory of spline-type (or principal shift invariant) spaces. As an extremely useful tool allowing to establish various kinds of robustness results we will present the so-called Wiener Amalgam spaces W (B, `), with ge...

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...

We study uniquely ergodic dynamical systems over locally compact, sigmacompact Abelian groups. We characterize uniform convergence in Wiener/Wintner type ergodic theorems in terms of continuity of the limit. Our results generalize and unify earlier results of Robinson and Assani respectively. We then turn to diffraction of quasicrystals and show how the Bragg peaks can be calculated via a Wiene...

This paper describes a certain part of Leonard Gross’s work in infinite-dimensional analysis, connected to the Gross Ergodicity Theorem. I then look at way in which Gross’s work helped to create a new subject within (mostly) finite-dimensional analysis, a subject which may be called “harmonic analysis with respect to heat kernel measure.” This subject transfers to Lie groups certain constructio...

Image acquisition devices are always subject to physical limitations that often manifest as distortions in the appearance of the captured image. The most common types of distortions can be divided into two categories: geometric and radiometric distortions. Examples of the latter ones are: changes in brightness, contrast, or illumination, sensor noise and blur. Since image blur can have many dif...