Basic relations valid for the Bernstein spaces $B^2_{\sigma}$ and their extensions to larger function spaces via a unified distance concept
Volume 102 / 2014
Banach Center Publications 102 (2014), 41-55
MSC: Primary 42A38; Secondary 30H10, 41A17, 46E35, 65D25, 94A20.
DOI: 10.4064/bc102-0-2
Abstract
Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_\sigma^p$ are no longer valid in larger spaces. However, when a function $f$ is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of $f$ from $B_\sigma^p$. The difficult situation of derivative-free error estimates is also covered.
