Related papers: Finite-dimensional approximations of push-forwards…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
We study the random sampling of the short-time Fourier transform of functions that are localized in a compact region in the time-frequency plane. We follow the approach introduced by Bass and Gr\"ochenig for band-limited functions, and show…
Description of linear continuous functionals on a space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in $\mathbb R^n$ in terms of their Fourier-Laplace transform is obtained.
We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of…
This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which attaches to any continuous representation of a…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
Approximative properties of the Taylor-Abel-Poisson linear summation me\-thod of Fourier series are considered for functions of several variables, periodic with respect to the hexagonal domain, in the integral metric. In particular, direct…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…
The Forward-Forward (FF) algorithm presents a compelling, bio-inspired alternative to backpropagation. However, while efficient in training, it has a computationally prohibitive inference process that requires a separate forward pass for…
The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
This manuscript proposes a class of fractional stochastic integro-differential equation (FSIDE) with non-instantaneous impulses in an arbitrary separable Hilbert space. We use a projection scheme of increasing sequence of finite dimensional…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet…