Polynomial approximations and universality

• Autorzy: A. Mouze
• Języki publikacji: EN

Abstrakty

EN

We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be deduced in a unified way.

Kategorie tematyczne

• 30K10: Universal Dirichlet series
• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 30E10: Approximation in the complex domain
• 30K05: Universal Taylor series
• 30B30: Boundary behavior of power series, over-convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 2
• Strony: 103-120

Daty

wydano

2010

Twórcy

autor

A. Mouze

• Laboratoire Paul Painlevé, UMR 8524
• École Centrale de Lille, Cité Scientifique, 59650 Villeneuve d'Ascq, France

Identyfikatory

DOI

10.4064/sm196-2-1