Related papers: Interpolation with a function parameter and refine…
Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities.
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
Let $\mathcal{H}$ be a separable complex Hilbert space. A conjugate-linear map $C:\mathcal{H}\to \mathcal{H}$ is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let…
We compute the K-functional related to some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of the previous works of the authors. This computation allows to determine the…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that…
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…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…
In this paper, we investigate the relationship between the Hilbert functions and the associated properties of the graded modules. To attain this, we construct the graded modules from the sets of points in projective space, $\mathbb{P}_k^n$…
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…
We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…
This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal…
We give a set of test functions for the interpolation problem on $H_1^\infty$ , the constrained interpolation problem studied by Davidson, Paulsen, Raghupathi and Singh. We show that this set of test functions is minimal.
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…
Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calder\'on products if both interpolants are separable. We show that one separability assumption may be omitted and establish a…
Polygons are compound geometric objects, but when trying to understand the expected behavior of a large collection of random polygons -- or even to formalize what a random polygon is -- it is convenient to interpret each polygon as a point…