Related papers: Chains of reproducing kernel Hilbert spaces genera…

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 construct new stable vector bundles on Hilbert schemes of points on algebraic surfaces, which are parametrised by connected components of their moduli spaces. This work generalises aspects of our previous work on tautological bundles and…

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system…

In this note, we compute the reproducing kernel for the RKHS of functions on $\mathbb{R}^n$ in a sufficiently high Sobolev norm.

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…

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…

Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the…

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…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…

In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann…

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…

We consider dynamical systems with boundary control associated with finite Jacobi matrices. Using the method previously developed by the authors, we associate with these systems special Hilbert spaces of analytic functions (de Branges…

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

The Fourier transform and its inverse are well-known to have complex conjugate integral kernels. S.~Saitoh demonstrated that this relationship extends to the theory of integral transforms of Hilbert spaces of functions under certain…

We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…

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…