Related papers: A Reproducing Kernel Condition for Indeterminacy i…
The nonlocal diffusion equation with continuous kernel $K(x,y$, with $ \int_{R} K(y,x) \, d \, y = 1$ has been proposed as a model for some evolution process with diffusion, including population models. However, in general, we don't have $…
Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…
All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality.…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
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…
A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…
This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace.…
We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…
This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is…
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…
We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific…
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore…
We study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a rational function and the measure is supported on some…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
We consider inverse eigenvalue problems for the perturbed Bessel operator in $L^{2}(0,1)$. (1) For the case where the angular-momentum quantum number $\ell\in\mathbb{N}\cup\{0\}$, we establish a uniqueness result for the inverse spectral…
We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In particular, we study a special solution called the canonical…