Basic relations valid for the Bernstein spaces $B²_{σ}$ and their extensions to larger function spaces via a unified distance concept

• Autorzy: P. L. Butzer , R. L. Stens , G. Schmeisser
• Języki publikacji: EN

Abstrakty

EN

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and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_σ^p$ are no longer valid in larger spaces.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

Kategorie tematyczne

• 94A20: Sampling theory
• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 30H10: Hardy spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 65D25: Numerical differentiation
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 102
• Numer: 1
• Strony: 41-55

Daty

wydano

2014

Twórcy

autor

P. L. Butzer

• Lehrstuhl A für Mathematik, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

autor

R. L. Stens

• Lehrstuhl A für Mathematik, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

autor

G. Schmeisser

• Department of Mathematics, University of Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen, Germany

Identyfikatory

DOI

10.4064/bc102-0-2