Some exact constants for bilateral approximations in quasi-normed groups
Functional Analysis
2024-10-22 v2
Abstract
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions in Lebesgue's spaces by decreasing rearrangements with the help of approximation -functionals, error estimates are found. Examples of numerical calculations and spectral approximations of self-adjoint operators obtained by obtained estimates are given.
Cite
@article{arxiv.2405.09775,
title = {Some exact constants for bilateral approximations in quasi-normed groups},
author = {Oleh Lopushansky},
journal= {arXiv preprint arXiv:2405.09775},
year = {2024}
}