Related papers: Positive Gaussian kernels also have Gaussian minim…

Among the various approaches for producing point distributions with blue noise spectrum, we argue for an optimization framework using Gaussian kernels. We show that with a wise selection of optimization parameters, this approach attains…

We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…

We study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities. In particular, we obtain explicit criteria for the solvability of the Dirichlet problem…

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…

In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give…

The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators play a significant role, the one which governs the operator…

In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of…

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…

The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of…

Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck…

This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…

Quasi-normal-eigenvalue optimization is studied under constraints $b_1(x) \le B(x) \le b_2 (x)$ on structure functions $B$ of 2-side open optical or mechanical resonators. We prove existence of various optimizers and provide an example when…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…

We consider a family of gradient Gaussian vector fields on $\Z^d$, where the covariance operator is not translation invariant. A uniform finite range decomposition of the corresponding covariance operators is proven, i.e., the covariance…

We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremum spaces with Lyapunov type functions and local domination.…

We consider positive semidefinite kernels which have values given by bounded linear operators on certain bundles of Hilbert spaces and which are invariant under actions of $*$-semigroupoids. For these kernels, we prove that there exist…

We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…

We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sided bounds for deviation from the median as well as from the…