0. Introduction. Let G be a locally compact Abelian group, and G* its group of (continuous) characters. We write (y, x) to indicate the function on G*XG which is the value of the character y EG* at the point *6G, or, dually, the value of the character xEG at the point y EG*. Borel sets in G are taken to be the smallest cr-algebra of sets containing all closed sets. We consider the set of all re...

Different generators of a deformed oscillator algebra give rise to oneparameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the q-coherent states and with ’coordinate’ operators Jacobi matrices, are also pointed out. Permanent add...

We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and Green’s operators, we employ the algebra of integro-differential operators. The operations implemented for regular boundary problems include computing Green’s ...

This article investigates the super-resolution phenomenon using the celebrated statistical estimator LASSO in the complex valued measure framework. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, Stieltjes transformation...). In particular, we provide an explicit quantitative localization of the spikes. Moreover, o...