Related papers: Interpolating sequences on the bidisk
Some notes and observations on analytic functions defined on an annulus
A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud., 4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc…
When we deal with $H^{\infty}$, it is known that $c_0-$interpolating sequences are interpolating and it is sufficient to interpolate idempotents of $\ell_\infty$ in order to interpolate the whole $\ell_\infty$. We will extend these results…
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a…
Three different characterizations of one-component bounded analytic functions are provided. The first one is related to the the inner-outer factorization, the second one is in terms of the size of the reproducing kernels in the…
We produce a Schwarz lemma for the symmetrized tridisc \[ \mathbb G_3 =\{ (z_1+z_2+z_3,z_1z_2+z_2z_3+z_3z_1,z_1z_2z_3): \,|z_i|< 1, i=1,2,3 \}. \] We show that an interpolating function related to the Schward lemma for $\mathbb G_3$ is not…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as…
Existing and extremal property of periodic perfect spline, which interpolates given function in the mean were proved.
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.
Construction of analytic functions, which determine bounded Toeplitz operators
We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
We describe the set of inner functions of finite order in a multi-connected domain, then we consider an optimization formulation of the Pick-Nevanlinna interpolation problem, and we generalize it to Hermite type interpolation.
We give a slight generalization of the characterization of finite Blaschke products given in a previous paper. The characterization uses the boundary behaviour of a weighted local hyperbolic distortion of an analytic self-map of the unit…
We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space of the bidisk if some associated function is a positive kernel. This positivity…