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

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

Basic relations valid for the Bernstein spaces

B ²_{σ}

and their extensions to larger function spaces via a unified distance concept

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

Banach Center Publications, Tome 102 (2014), p. 41-55 / Harvested from The Polish Digital Mathematics Library

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Résumé

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formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces $B_{σ}^{p}$ are no longer valid in larger spaces.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

Publié le : 2014-01-01

Zbl 1315.42014

EUDML-ID : urn:eudml:doc:282009

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     author = {P. L. Butzer and R. L. Stens and G. Schmeisser},
     title = {Basic relations valid for the Bernstein spaces $B$^2$\_{$\sigma$}$ and their extensions to larger function spaces via a unified distance concept},
     journal = {Banach Center Publications},
     volume = {102},
     year = {2014},
     pages = {41-55},
     zbl = {1315.42014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-2}
}

P. L. Butzer; R. L. Stens; 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, Tome 102 (2014) pp. 41-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-2/