Related papers: Reproducing kernel Hilbert spaces generated by the…

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…

We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of…

Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…

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…

We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that…

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.

We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…

We introduce a family of reproducing kernel Hilbert spaces $\mathcal A_\Lambda$ of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb{H}$. The reproducing kernel of $\mathcal A_\Lambda$…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…

Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

We show that polynomials do not belong to the reproducing kernel Hilbert space of infinitely differentiable translation-invariant kernels whose spectral measures have moments corresponding to a determinate moment problem. Our proof is based…

In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized…