相关论文: Hilbert Spaces Contractively Contained in Weighted…

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels 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…

In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\mathcal{D}(\mu)$ in terms of the boundary spectrum of $b$ and the support of the measure $\mu$, by using elementary…

Weighted discrete Hilbert transforms $(a_n)_n \mapsto \sum_n a_n v_n/(z-\gamma_n)$ from $\ell^2_v$ to a weighted $L^2$ space are studied, with $\Gamma=(\gamma_n)$ a sequence of distinct points in the complex plane and $v=(v_n)$ a…

In the Clifford algebra setting the present study develops three reproducing kernel Hilbert spaces of the Paley-Wiener type, namely the Paley-Wiener spaces, the Hardy spaces on strips, and the Bergman spaces on strips. In particular, we…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).

We introduce new functional spaces that generalize the weighted Bergman and Dirichlet spaces on the disk D(0,R) in the complex plane and the Bargmann-Fock spaces on the whole complex plane. We give a complete description of the considered…

We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges-Rovnyak space ${\mathcal H}(K_{S})$ as the state space for the unique (up to…

We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…

Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured…

We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to…

A weighted composition operator on a reproducing kernel Hilbert space is given by a composition, followed by a multiplication. We study unitary and co-isometric weighted composition operators on unitarily invariant spaces on the Euclidean…

In this paper we deal with a scale of reproducing kernel Hilbert spaces $H^{(n)}_2$, $n\ge 0$, which are linear subspaces of the classical Hilbertian Hardy space on the right-hand half-plane $\mathbb{C}^+$. They are obtained as ranges of…

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

We show that if a reproducing kernel Hilbert space $H_K,$ consisting of functions defined on ${\bf E},$ enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Condition (LIC), then for any preset natural number $n,$ and…

Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…