Related papers: Complete interpolating sequences for the Gaussian …
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…
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…
We present an invariant density for the finite Gauss transformation of the unit interval and discuss some properties of this transformation.
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,…
In this paper, we study the problem of interpolating a continuous function at $(n+1)$ equally-spaced points in the interval $[0,1]$, using shifts of a kernel on the $(1/n)$-spaced infinite grid. The archetypal example here is approximation…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
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 characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.
Let $V^p_\Gamma(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $\Gamma$-shifts of a function $\mathcal{G}$, where $\Gamma\subset\mathbb{R}$ is a separated set. For several large families of generators…
We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a…
We study extra time-frequency shift invariance properties of Gabor spaces. For a Gabor space generated by an integer lattice, we state and prove several characterizations for its time-frequency shift invariance with respect to a finer…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so…
Necessary and sufficient conditions are given for density of shift-invariant subspaces of the space $\mathcal{L}$ of integrable functions of bounded support with the inductive limit topology.
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
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…