Related papers: Interpolating sequences in spaces with the complet…
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…
We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.
We prove that under the extended Carleson's condition, a sequence $(x_n) \subset B_H$ is linear interpolating for $H^{\infty}(B_H)$ for an infinite dimensional Hilbert space H. In particular, we construct the interpolating functions for…
We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces $H^p(\mathbb{D}^d)$ on the polydisc. In dimension $d=1$ a sequence is simply interpolating if and only if it is universally…
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…
Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the…
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…
Let $S$ be a sequence of points in ${\mathbb{D}}^{n}.$ Suppose that $S$ is $H^{p}$ interpolating. Then we prove that the sequence $S$ is Carleson, provided that $p>2.$ We also give a sufficient condition, in terms of dual boundedness and…
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…
We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the…
We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.
In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.
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…
We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form $k(s,u) = \sum a_n n^{-s-\bar u}$, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing…
Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^{n}.$ Denote $H^{p}$($\Omega $) the Hardy space of $\Omega .$ Suppose that $S$ is $H^{p}$ interpolating with $p\geq 2.$ Then…
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…
This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We…
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…
We discuss random interpolation in weighted Dirichlet spaces $\mathcal{D}_\alpha$, $0\leq \alpha\leq 1$. While conditions for deterministic interpolation in these spaces depend on capacities which are very hard to estimate in general, we…
We characterise interpolating and sampling sequences for the spaces of entire functions f such that f e^{-phi} belongs to L^p(C), p>=1 (and some related weighted classes), where phi is a subharmonic weight whose Laplacian is a doubling…