JEDNOSTKA NAUKOWA KATEGORII A+

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

Tom 102 / 2014

P. L. Butzer, R. L. Stens, G. Schmeisser Banach Center Publications 102 (2014), 41-55 MSC: Primary 42A38; Secondary 30H10, 41A17, 46E35, 65D25, 94A20. DOI: 10.4064/bc102-0-2

Streszczenie

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formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_\sigma^p$ are no longer valid in larger spaces.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

Autorzy

  • P. L. ButzerLehrstuhl A für Mathematik
    RWTH Aachen University
    Templergraben 55
    52062 Aachen, Germany
    e-mail
  • R. L. StensLehrstuhl A für Mathematik
    RWTH Aachen University
    Templergraben 55
    52062 Aachen, Germany
    e-mail
  • G. SchmeisserDepartment of Mathematics
    University of Erlangen-Nuremberg
    Cauerstr. 11
    91058 Erlangen, Germany
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek