Related papers: Embeddings of Reproducing Kernel Hilbert Spaces wi…
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.
The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…
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…
We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
In this paper, we define and study a nested family of reproducing kernel Hilbert spaces of vector fields that is indexed by a range of scales, from which we construct a reproducing kernel Hilbert space of scale-dependent vector fields. We…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
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 $\mathcal A_\Lambda$…
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…
Let $(X,\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak and strong are all equivalents. From this we describe some important consequences…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the Euclidean Motion $SE(2)$. A natural Hilbert norm for functions on…
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…
By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of $n$-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…
This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…
In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate 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…