Related papers: Infinite product representations for kernels and i…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
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…
Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…
In this paper we are discussing various aspects of wavelet filters. While there are earlier studies of these filters as matrix valued functions in wavelets, in signal processing, and in systems, we here expand the framework. Motivated by…
This note consists of two largely independent parts. In the first part we give conditions on the kernel $k: \Omega \times \Omega \rightarrow \mathbb{R}$ of a reproducing kernel Hilbert space $H$ continuously embedded via the identity…
By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…
It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we…
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…
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…
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space $X$into $\mathbb C^n$. Given a finite measure $\mu$ on $X$, we represent the reproducing kernel $K$ as…
We study kernel functions of L-functions and products of L-functions of Hilbert cusp forms over real quadratic fields. This extends the results on elliptic modualr forms by Diamantis and C. O'Sullivan. .
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
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…
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…
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…
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…