# Basic relations valid for the Bernstein spaces $B{\xb2}_{\sigma}$ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer; R. L. Stens; G. Schmeisser

Banach Center Publications (2014)

- Volume: 102, Issue: 1, page 41-55
- ISSN: 0137-6934

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topP. 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and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_σ^p$ are no longer valid in larger spaces.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and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_σ^p$ are no longer valid in larger spaces.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 -

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