English

Approximation by linear sampling operators in Banach spaces

Functional Analysis 2026-01-28 v1 Numerical Analysis Classical Analysis and ODEs Numerical Analysis

Abstract

This paper studies approximation properties of linear sampling operators in general Banach lattices XX. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special KK-functionals and their realizations by sampling operators, as well as strong converse inequalities, which, to the best of our knowledge, have not been previously established for sampling operators even in the classical spaces LpL_p. The results extend several classical theorems previously known mainly in LpL_p and apply to all functions fXf\in X for which the corresponding sampling operator is well defined, thereby substantially enlarging the class of functions that can be considered in this framework.

Keywords

Cite

@article{arxiv.2601.19012,
  title  = {Approximation by linear sampling operators in Banach spaces},
  author = {Yurii Kolomoitsev},
  journal= {arXiv preprint arXiv:2601.19012},
  year   = {2026}
}
R2 v1 2026-07-01T09:21:20.957Z