Related papers: Density results for continuous frames
We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…
We provide general conditions to derive posterior concentration rates for Aalen counting processes. The conditions are designed to resemble those proposed in the literature for the problem of density estimation, for instance in Ghosal et…
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
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…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.
Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
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…
In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators,…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…
This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.