Related papers: Interpolating sequences on the bidisk

We introduce the notion of cascade connection of multiparametric discrete time-invariant linear dynamical systems with unit delay. This allows us to construct the explicit example of conservative realization of a decomposable…

In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…

In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…

An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the authors. We use the asymptotic Samuel function to give the…

We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0)=0.$ Alternatively, these results can be interpreted as…

We study simply interpolating sequences for the Dirichlet space in the unit disc. In particular we are interested in comparing three different sufficient conditions for simply interpolating sequences. The first one is the the so called one…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

In this paper we study the action of a generalization of the Binomial interpolated operator on the set of linear recurrent sequences. We find how the zeros of characteristic polynomials are changed and we prove that a subset of these…

This note presents a simple approach to proving the interlacing properties of positive zeros of Bessel functions of the first kind. The approach relies only on the standard recurrence relations between Bessel functions and characterising…

We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities.

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.

The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of…

A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…

A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have…

We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators.

The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…

We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and \O yma about interpolating sequences in the same spaces, and it…

The one-dimensional pseudo Leja sequences introduced in \cite{bialas2012pseudo}, as an alternative to Leja sequences, provides us with good interpolation nodes for the approximation of holomorphic functions. We propose a definition of…

In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sierpi\'nski gaskets. Further, we collect some results regarding smoothness of the constructed FIF. We prove, in particular, that the FIF are…