Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings

2020/02/24 by Michael I. Ganzburg, Ganzburg, Michael I.
Mathematics · #41A63 #41A65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Primary 41A44 #Secondary 41A17

paper · pdf · doi:10.48550/arxiv.2002.10512

openalex publication_date 2020/02/24 · openalex created_date 2023/01/03 · openalex updated_date 2026/07/28

Abstract

In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements, and approximation on classes of elements. Second, we find sufficient conditions that imply limit relations between various sharp constants of approximation theory in general settings. Third, a number of examples from various areas of approximation theory illustrates the general approach.

Related

• Sharp bounds for symmetric and asymmetric Diophantine approximation
• Approximation systems
• Lower bounds on the two-sided inhomogeneous approximation constant
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