Basic relations valid for the Bernstein spaces $B{²}_{\sigma }$ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, and G. Schmeisser. "Basic relations valid for the Bernstein spaces $B²_{σ}$ and their extensions to larger function spaces via a unified distance concept." Banach Center Publications 102.1 (2014): 41-55. <http://eudml.org/doc/282009>.

@article{P2014,
abstract = {Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_σ^p$ are no longer valid in larger spaces.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 $B_σ^p$. The difficult situation of derivative-free error estimates is also covered.},
author = {P. L. Butzer, R. L. Stens, G. Schmeisser},
journal = {Banach Center Publications},
keywords = {Bernstein spaces; Sobolev spaces; modulation spaces; Hardy spaces; bandlimited functions; non-bandlimited functions; derivative-free error estimates; sampling formula; differentiation formula; Poisson summation formula; reproducing kernel formula; general Parseval formula; Bernstein inequality},
language = {eng},
number = {1},
pages = {41-55},
title = {Basic relations valid for the Bernstein spaces $B²_\{σ\}$ and their extensions to larger function spaces via a unified distance concept},
url = {http://eudml.org/doc/282009},
volume = {102},
year = {2014},
}

TY - JOUR
AU - P. L. Butzer
AU - R. L. Stens
AU - G. Schmeisser
TI - Basic relations valid for the Bernstein spaces $B²_{σ}$ and their extensions to larger function spaces via a unified distance concept
JO - Banach Center Publications
PY - 2014
VL - 102
IS - 1
SP - 41
EP - 55
AB - Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_σ^p$ are no longer valid in larger spaces.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 $B_σ^p$. The difficult situation of derivative-free error estimates is also covered.
LA - eng
KW - Bernstein spaces; Sobolev spaces; modulation spaces; Hardy spaces; bandlimited functions; non-bandlimited functions; derivative-free error estimates; sampling formula; differentiation formula; Poisson summation formula; reproducing kernel formula; general Parseval formula; Bernstein inequality
UR - http://eudml.org/doc/282009
ER -