Related papers: Finite-dimensional approximations of push-forwards…
Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analytic functions of countably infinite number of variables.…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
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…
We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…
Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…
We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…
In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we…
In recent years, there has been growing interest in the field of functional neural networks. They have been proposed and studied with the aim of approximating continuous functionals defined on sets of functions on Euclidean domains. In this…
In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…
Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…
In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for functions of finite energy in several complex and several real…
Functional data analysis is typically conducted within the $L^2$-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems,…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tseng's…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space. To this end, we use an additive family to map the input…