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A Sharp Constant in the Estimation of the Error of the Approximation of Classes of Differentiable Functions by the Second-Order Cesáro Means
AbstractWe consider the problem of finding a sharp constant in the approximation of continuous functions by linear methods. The best constant is...
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Sharp unifying generalizations of Opial’s inequality
Opial’s inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying...
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Sharp Inequalities for Linear Combinations of Orthogonal Martingales
For any two real-valued continuous-path martingales X = { X t } t ≥0 and Y = { Y t } t ≥0 , with X and Y being orthogonal and Y being differentially subordinate...
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On the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces
We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some...
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Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation...
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Sharp bounds for Hardy-type operators on mixed radial-angular central Morrey spaces
By using the rotation method, a sharp bound for an n -dimensional Hardy operator on mixed radial-angular central Morrey spaces is obtained....
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Finite Convergence and Sharp Minima for Quasi-Equilibrium Problems
The notion of sharp minima, given by Polyak, is an important tool in studying the convergence analysis of algorithms designed to solve optimization...
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Some Sharp Bohr-Type Inequalities for Analytic Functions
This article focuses on the improvement of the classic Bohr’s inequality for bounded analytic functions on the unit disk. We give some sharp versions...
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Lieb–Thirring Inequalities on Manifolds with Constant Negative Curvature
In this short note, we prove Lieb–Thirring inequalities on manifolds with negative constant curvature. The discrete spectrum appears below the...
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Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
We investigate whether a fundamental solution of the Schrödinger equation ∂ t u = (Δ + V ) u has local in time sharp Gaussian estimates. We compare that...
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Sharp Second-Order Adams Inequalities in Lorentz–Sobolev Spaces
In this paper, we establish sharp subcritical and critical second-order Adams inequalities in Lorentz–Sobolev spaces. We also prove the subcritical...
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Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion
This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP...
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Uniform Upper Bounds on Courant Sharp Neumann Eigenvalues of Chain Domains
We obtain upper bounds on the number of nodal domains of Laplace eigenfunctions on chain domains with Neumann boundary conditions. The chain domains...
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Sharp Pitt’s inequality and Beckner’s logarithmic uncertainty principle for the Weinstein transform
In this paper, we prove the sharp Pitt’s inequality for the Weinstein transform. As an application, the Beckner’s logarithmic uncertainty principle...
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Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves
This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a...
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Stochastic algorithms with geometric step decay converge linearly on sharp functions
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size...
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Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures
We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al....
