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Related papers: Random interpolating sequences in Dirichlet spaces

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We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…

Complex Variables · Mathematics 2012-10-17 Jan-Fredrik Olsen , Kristian Seip

We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the…

Complex Variables · Mathematics 2021-07-13 Alberto Dayan , Brett D. Wick , Shengkun Wu

We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler…

Functional Analysis · Mathematics 2023-06-27 Nikolaos Chalmoukis , Alberto Dayan , Michael Hartz

We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of…

Probability · Mathematics 2013-09-20 Christophe Sabot , Laurent Tournier

We study random interpolating sequences with prescribed radii in the Nevanlinna and Smirnov classes. As it turns out these are characterized by the Blaschke condition. This follows from a more general result. Indeed, we show that this…

Complex Variables · Mathematics 2026-01-06 Giuseppe Lamberti

Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with…

Complex Variables · Mathematics 2013-02-05 Andreas Hartmann

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…

Complex Variables · Mathematics 2007-05-23 Alexander P. Schuster , Dror Varolin

If $\alpha$ is a probability on $\mathbb{R}^d$ and $t>0,$ consider the Dirichlet random probability $P_t\sim\mathcal{D}(t\alpha) ;$ it is such that for any measurable partition $(A_0,\ldots,A_k)$ of $\mathbb{R}^d$ then…

Probability · Mathematics 2014-05-20 Gerard Letac , Mauro Piccioni

The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…

Complex Variables · Mathematics 2025-12-11 Andreas Hartmann , Giuseppe Lamberti

Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights $(1-|z|)^{-\alpha}$, $0<\alpha<1$. These results…

Complex Variables · Mathematics 2014-12-10 Kristian Seip

Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in…

Functional Analysis · Mathematics 2021-01-11 Frédéric Bayart

We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space $H_1(\mathbb{D})$ we define a natural notion of onto interpolation and we…

Complex Variables · Mathematics 2023-05-05 Nikolaos Chalmoukis

The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient…

Complex Variables · Mathematics 2014-12-10 Kristian Seip

The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…

Probability · Mathematics 2019-11-07 Rémy Poudevigne

Unevenly spaced samples from a periodic function are common in signal processing and can often be viewed as a perturbed equally spaced grid. In this paper, we analyze how the uneven distribution of the samples impacts the quality of…

Numerical Analysis · Mathematics 2023-04-11 Annan Yu , Alex Townsend

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized…

Probability · Mathematics 2016-02-01 Christophe Sabot , Laurent Tournier

We study thin interpolating sequences $\{\lambda_n\}$ and their relationship to interpolation in the Hardy space $H^2$ and the model spaces $K_\Theta = H^2 \ominus \Theta H^2$, where $\Theta$ is an inner function. Our results, phrased in…

Complex Variables · Mathematics 2016-01-19 Pamela Gorkin , Brett D. Wick

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…

Complex Variables · Mathematics 2022-02-17 Alejandro Miralles , Mario P. Maletzki

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…

Numerical Analysis · Mathematics 2023-03-27 Francesco Dell'Accio , Alvise Sommariva , Marco Vianello

We consider one-dependent random walks on $\mathbb{Z}^d$ in random hypergeometric environment for $d\ge 3$. These are memory-one walks in a large class of environments parameterized by positive weights on directed edges and on pairs of…

Probability · Mathematics 2020-08-10 Tal Orenshtein , Christophe Sabot
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