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Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
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…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left…
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
Integral operators play a central role in signal processing, underpinning classical convolution, and filtering on continuous network models such as graphons. While these operators are traditionally analyzed through spectral decompositions,…
The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
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 is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…