Related papers: The reproducing kernel thesis for lower bounds of …

This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…

We consider restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer trained by an unlabelled dataset composed of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to…

This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…

The Berezin range of a bounded operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}$ is the set $\text{Ber}(T)$ := $\{\langle T\hat{k}_{x},\hat{k}_{x} \rangle_{\mathcal{H}} : x \in X\}$, where $\hat{k}_{x}$ is the…

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We completely characterized every case of the bounded and compact Toeplitz operators on the weighted Bergman…

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…

Designing categorical kernels is a major challenge for Gaussian process regression with continuous and categorical inputs. Despite previous studies, it is difficult to identify a preferred method, either because the evaluation metrics, the…

In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…

In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also…

We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of…

We use a classical characterisation to prove that functions which are bounded away from zero cannot be elements of reproducing kernel Hilbert spaces whose reproducing kernels decays to zero in a suitable way. The result is used to study…

The reproducing kernel function of a weighted Bergman space over domains in ${\mathbb C}^d$ is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of codimension…

In 1955 Kadison \cite{14} asked whether the analogue of the classical Burnside's theorem of the Linear Algebra holds in the infinite dimensional case. We use reproducing kernels method to solve the Kadison question. Namely, we prove that…

Sub-Bergman Hilbert spaces are analogues of de Branges-Rovnyak spaces in the Bergman space setting. They are reproducing kernel Hilbert spaces contractively contained in the Bergman space of the unit disk. K. Zhu analyzed sub-Bergman…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…