Explanipedia

Universal discretization and sparse recovery Open

Feng Dai, Vladimir Temlyakov · 2025

Capacity Configuration of Microgrids in Hydrogen Energy Storage Parks Based on Waste Heat Recovery Open

Hsin-Yu Yao, Yan Wang, Yifan Wei, Ji Fan, Wanqing Yuyang , et al. · 2025

Optimal Polynomial Meshes Exist on any Multivariate Convex Domain Open

Feng Dai, Andriy Prymak · 2023

Polynomial approximation on $C^2$-domains Open

Feng Dai, Andriy Prymak · 2022

We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact $C^2$-domain $Ω\subset \mathbb{R}^d$. This new modulus of smoothness is defined …

Sampling discretization of integral norms and its application Open

Feng Dai, Vladimir Temlyakov · 2021

The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions -- condit…

𝐿^{𝑝}-Bernstein inequalities on 𝐶²-domains and applications to discretization Open

Feng Dai, Andriy Prymak · 2021

We prove a new Bernstein type inequality in spaces associated with the normal and the tangential derivatives on the boundary of a general compact -domain. We give two applications: Marcinkiewicz type inequality for discretization of norm…

Universal sampling discretization Open

Feng Dai, Vladimir Temlyakov · 2021

Let $X_N$ be an $N$-dimensional subspace of $L_2$ functions on a probability space $(Ω, μ)$ spanned by a uniformly bounded Riesz basis $Φ_N$. Given an integer $1\leq v\leq N$ and an exponent $1\leq q\leq 2$, we obtain universal discretizat…

Discretization of integrals on compact metric measure spaces Open

Martin Buhmann, Feng Dai, Yeli Niu · 2021

L p -Bernstein inequalities on C 2 -domains. Open

Feng Dai, Andriy Prymak · 2020

We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm…

$L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization Open

Feng Dai, Andriy Prymak · 2020

We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm…

Entropy numbers and Marcinkiewicz-type discretization theorem Open

Feng Dai, Andriy Prymak, Alexei Shadrin, Vladimir Temlyakov, Sergey Tikhonov · 2020

This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied …

Sampling discretization of integral norms Open

Feng Dai, Andriy Prymak, Alexei Shadrin, Vladimir Temlyakov, Sergey Tikhonov · 2020

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this paper we obta…

Polynomial approximation on $C^2$-domains Open

Feng Dai, Andriy Prymak · 2019

We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact $C^2$-domain $Ω\subset \mathbb{R}^d$. This new modulus of smoothness is defined …

Integral norm discretization and related problems Open

Feng Dai, Andriy Prymak, Vladimir Temlyakov, Sergey Tikhonov · 2019

The problem is discussed of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure. This problem is investigated for elements of finite-dimensional space…

Estimates of the asymptotic Nikolskii constants for spherical polynomials Open

Feng Dai, Д. В. Горбачев, Sergey Tikhonov · 2019

Let $Π_n^d$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $\mathbb{S}^d\subset \mathbb{R}^{d+1}$ that is equipped with the surface Lebesgue measure $dσ$ normalized by $\int_{\mathbb{S}^d} \, dσ(x)=1$. T…

Nikolskii constants for polynomials on the unit sphere Open

Feng Dai, Д. В. Горбачев, Sergey Tikhonov · 2017

This paper studies the asymptotic behavior of the exact constants of the Nikolskii inequalities for the space $Π_n^d$ of spherical polynomials of degree at most $n$ on the unit sphere $\mathbb{S}^d\subset \mathbb{R}^{d+1}$ as $n\to\infty$.…

Stolarsky principle and energy optimization on the sphere Open

Dmitriy Bilyk, Feng Dai, Ryan Matzke · 2016

The classical Stolarsky invariance principle connects the spherical cap $L^2$ discrepancy of a finite point set on the sphere to the pairwise sum of Euclidean distances between the points. In this paper we further explore and extend this p…

Littlewood-Paley Characterizations of Fractional Sobolev Spaces via Averages on Balls Open

Feng Dai, Jun Liu, Dachun Yang, Wen Yuan · 2015

In this paper, the authors characterize Sobolev spaces $W^{α,p}({\mathbb R}^n)$ with the smoothness order $α\in(0,2]$ and $p\in(\max\{1, \frac{2n}{2α+n}\},\infty)$, via the Lusin area function and the Littlewood-Paley $g_λ^\ast$-function i…

Characterizations of Besov and Triebel-Lizorkin Spaces via Averages on Balls Open

Feng Dai, Амиран Гогатишвили, Dachun Yang, Wen Yuan · 2015

Let $\ell\in\mathbb{N}$ and $p\in(1,\infty]$. In this article, the authors prove that the sequence $\{f-B_{\ell,2^{-k}}f\}_{k\in\mathbb{Z}}$ consisting of the differences between $f$ and the ball average $B_{\ell,2^{-k}}f$ characterizes th…

Erratum to: The Hardy–Rellich Inequality and Uncertainty Principle on the Sphere Open

Feng Dai, Yuan Xu · 2015

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