Related papers: Sampling and interpolation for analytic selfmappin…
We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
We introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective…
The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…
For an inner function $\theta$ with $\theta'\in\mathcal N$, where $\mathcal N$ is the Nevanlinna class, several problems are posed in connection with the canonical (inner-outer) factorization of $\theta'$.
In this article, we establish a connection between Pick bodies and invariant functions. We demonstrate that an invariant function can be associated with any Pick body, which determines the solvability of a given Pick interpolation problem…
We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities…
We extend the study of the Pick class, the set of complex analytic functions taking the upper half plane into itself, to the noncommutative setting. R. Nevanlinna showed that elements of the Pick class have certain integral representations…
The classical theorems of Mittag-Leffler and Weierstrass show that when $\{\lambda_n\}$ is a sequence of distinct points in the open unit disk $\D$, with no accumulation points in $\D$, and $\{w_n\}$ is any sequence of complex numbers,…
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on…
We provide a necessary condition for the existence of a 3-point holomorphic interpolant $F:\mathbb{D}\longrightarrow\Omega_n$, $n\geq 2$. Our condition is inequivalent to the necessary conditions hitherto known for this problem. The…
In this paper we prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n.
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
A map on a group into itself is called a local automorphism if at any two points of the group, it can be interpolated by an automorphism of that group. In this paper we investigate the question of how local automorphisms of some classical…
Indefinite Schwarz-Pick inequalities for holomorphic self-maps of the bidisk are given as application of the spectral theory on Hilbert modules.
We study multiple sampling and interpolation problems with unbounded multiplicities in the weighted Bergman space, both in the hilbertian case p = 2 and the uniform case p = +$\infty$.
Agler and McCarthy studied the uniqueness of a 3-point interpolation problem in the bidisc. This note aims to solve an analogous problem in the unit Euclidean ball in an arbitrary dimension.
Graph sampling set selection, where a subset of nodes are chosen to collect samples to reconstruct a smooth graph signal, is a fundamental problem in graph signal processing (GSP). Previous works employ an unbiased least-squares (LS) signal…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…