Related papers: Complete Interpolating sequences for small Fock Sp…

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 obtain a complete characterization of the entire functions $g$ such that the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$, induced by…

A sequence which is a finite union of interpolating sequences for $H^\infty$ have turned out to be especially important in the study of Bergman spaces. The Blaschke products $B(z)$ with such zero sequences have been shown to be exactly…

We consider the Fock space weighted by $e^{-\alpha |z|^{2}}$, of entire and quasi-periodic (modulo a weight dependent on $\nu $) functions on ${C}$. The quotient space $\mathbb{C}/\mathbb{Z}$, called `The flat cylinder', is represented by…

For several shift-invariant spaces, there exists a real number $a\in\mathbb{R}$ such that the set $a+\mathbb{Z}$ is a complete interpolation set. In this paper, we characterize the complete interpolation property of the set…

In this paper we introduce a Fock space related to derivatives of Gelfond-Leontiev type, a class of derivatives which includes many classic examples like fractional derivatives or Dunkl operators. For this space we establish a modified…

We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.

We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This…

We investigate the convergence of entire Lagrange interpolations and of Hermite interpolations of exponential type in weighted $L^p$-spaces on the real line. The weights are reciprocals of entire functions and depend on the type and may be…

We study the uniqueness sets, the weak interpolation sets, and convergence of the Lagrange interpolation series in radial weighted Fock spaces

The author showed that a sequence in the unit disk is a zero sequence for the Bergman space $A^p$ if and only if a certain weighted space $L^p(W}$ contains a nontrivial analytic function. In this paper it is shown that the sequence is an…

In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and $H^p$ spaces. We extend the notion of asymptotic interpolation to $H^p$ spaces, for $1 \leq…

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 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…

Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not…

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…

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…

Let $E, F, E_0, E_1$ be rearrangement invariant spaces; let $a, \mathrm{b}, \mathrm{b}_0, \mathrm{b}_1$ be slowly varying functions and $0< \theta_0,\theta_1<1$. We characterize the interpolation spaces $$\Big(\overline{X}^{\mathcal…

We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…

In 2002 A.\ Hartmann and X.\ Massaneda obtained necessary and sufficient conditions for interpolation sequences for classes of analytic functions in the unit disc such that $\log M(r,f)=O((1-r)^{-\rho})$, $0<r<1$, $\rho \in (0 , +\infty)$,…