Related papers: Almost diagonal matrices and Besov-type spaces bas…

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…

The objective of the paper is to describe Besov spaces on general compact Riemannian manifolds in terms of the best approximation by eigenfunctions of elliptic differential operators.

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…

This paper is concerned with the study of Besov-type decomposition spaces, which are scales of spaces associated to suitably defined coverings of the euclidean space $\mathbb{R}^d$, or suitable open subsets thereof. A fundamental problem in…

This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are…

In this work we establish a sampling theorem for functions in Besov spaces on spaces of homogeneous type as defined in [HY] in the spirit of their recent counterpart for R d established by Jaming-Malinnikova in [JM]. The main tool is the…

We investigate Besov spaces of self-affine tilings of ${\Bbb R}^{n}$ and discuss various characterizations of those Besov spaces. We see what is a finite set of functions which generates the Besov spaces from a view of multiresolution…

In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the $\varphi $-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…

Let $\xi = \{x^j\}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\II}^d:=[0,1]^d$, and $\Phi = \{\phi_j\}_{j =1}^n$ a family of $n$ functions on ${\II}^d$. We define the linear sampling algorithm $L_n(\Phi,\xi,\cdot)$ for an…

Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular we obtain the…

In this article, the authors introduce Besov-type spaces with variable smoothness and integrability. The authors then establish their characterizations, respectively, in terms of $\varphi$-transforms in the sense of Frazier and Jawerth,…

We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain…

We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…

Let ${\mathcal {X}}$ be a space of homogeneous type. In this article, based on the reducing operators of matrix $A_p$-weights, the authors introduce the vector-valued Haj\l asz gradient sequences and establish some related matrix-weighted…

This work presents a systematic analysis and extension of the sparse radial basis function network (SparseRBFnet) previously introduced for solving nonlinear partial differential equations (PDEs). Based on its adaptive-width shallow kernel…

The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders…

Given any smooth Anosov map we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that in the case of expanding maps it reduces exactly to the usual space of functions of…

Inspired by the Kolmogorov-Arnold superposition theorem, Kolmogorov-Arnold Networks (KANs) have recently emerged as an improved backbone for most deep learning frameworks, promising more adaptivity than their multilayer perceptron (MLP)…

In this paper, we study a newly developed shearlet system on bounded domains which yields frames for $H^s(\Omega)$ for some $s\in \mathbb{N}$, $\Omega \subset \mathbb{R}^2$. We will derive approximation rates with respect to $H^s(\Omega)$…

We introduce the notion of approximate norm attainment set of a bounded linear operator between Banach spaces and use it to obtain a complete characterization of smooth points in the space of compact linear operators, provided the domain…