Sampling, interpolation and Riesz bases in small Fock spaces

Sampling and Interpolation in Bargmann-fock Spaces of Polyanalytic Functions

We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

Circle Packing and Interpolation in Fock Spaces

It was shown by James Tung in 2005 that if a sequence Z = {zn} of points in the complex plane satisfies inf n6=m |zn − zm| > 2/ √ α, then Z is a sequence of interpolation for the Fock space F p α . Using results from circle packing, we show that the constant above can be improved to √ 2π/( √ 3α), which is strictly smaller than 2/ √ α. A similar result will also be obtained for sampling sequences.

Riesz Bases in Sobolev Spaces 1792 Hb

On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...