Related papers: Interpolation without Separation in Bergman Spaces
Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism…
We find necessary density conditions for Marcinkiewicz-Zygmund inequalities and interpolation for spaces of spherical harmonics with respect to the L^p norm. Moreover, we prove that there are no complete interpolation families for p\neq 2.
In this paper, we investigate the $\partial$-complex on weighted Bergman spaces on Hermitian manifolds satisfying a certain holomorphicity/duality condition. This generalizes the situation of the Segal-Bargmann space in $\mathbb{C}^n$,…
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…
If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to $X\oplus V$, and any intermediate space obtained using the…
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.
Given n general points p_1, p_2,..., p_n in P^r, it is natural to ask when there exists a curve C \subset P^r, of degree d and genus g, passing through p_1, p_2,..., p_n. In this paper, we give a complete answer to this question for curves…
Long-baseline interferometry will be possible using pre-shared entanglement between two telescope sites to mimic the standard phase-scanning interferometer, but without physical beam combination. We show that spatial-mode sorting at each…
Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an…
We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…
It is well known that on arbitrary metric measure spaces, the notion of minimal $p$-weak upper gradient may depend on $p$. In this paper we investigate how a first-order condition of the metric-measure structure, that we call Bounded…
We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric…
Let $H$ be an infinite dimensional Hilbert space. We show that there exists a subspace of $B(H)$ which is isometric to $\ell_2$ and completely isometric to its antidual in the sense of the theory of operator spaces recently developed by…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…
We give three characterizations of the Dirichlet-type spaces $D(\mu)$. First we characterize $D(\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives.…
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…
Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an \emph{$M$-interpolation set} if given any function $g\in M^Y$…
The class $Ts(r,f)$ the trigonometric interpolation splines depending on the parameter vectors, selected convergence factors and interpolation factors is considered. The main properties of simple interpolation trigonometric splines are…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…