Related papers: Sampling in de Branges Spaces and Naimark Dilation
We show that a class of de Branges spaces, generated by means of generalized Fourier transforms associated with perturbed Bessel differential equations, has the properties of oversampling and aliasing.
Using the Naimark dilation theory we investigate the question under what conditions an observable which is a coarse graining of another observable is a function of it. To this end, conditions for the separability and for the Boolean…
This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by…
The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also…
We characterize an arbitrary de Branges space with bi-Lipschitz phase for large distances as a subspace of a weighted Paley--Wiener space, consisting of the elements square-integrable against a heavier weight on the real line.
Given a set $S$ of small measure, we discuss existence of sampling sequences for the Paley-Wiener space $PW_S$, which have both densities and sampling bounds close to the optimal ones.
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 study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…
Inspired by the work of Hedenmalm, Lindqvist and Seip, we consider different properties of dilations systems of a fixed function $\varphi \in L^2(0,1)$. More precisely, we study when the system $\{\varphi(nx)\}_n$ is a Bessel sequence, a…
Advances in techniques for thermal sampling in classical and quantum systems would deepen understanding of the underlying physics. Unfortunately, one often has to rely solely on inexact numerical simulation, due to the intractability of…
In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\mathcal{D}(\mu)$ in terms of the boundary spectrum of $b$ and the support of the measure $\mu$, by using elementary…
In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part,…
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…
We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the…
In the framework of a strictly local regular Dirichlet space ${\bf X}$ we introduce the subspaces $PW_{\omega},\>\>\omega>0,$ of Paley-Wiener functions of bandwidth $\omega$. It is shown that every function in $PW_{\omega},\>\>\omega>0,$ is…
A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such…