Generic properties of Padé approximants and Padé universal series

We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complemen...

Full description

Saved in:
Bibliographic Details
Published inMathematische Zeitschrift Vol. 281; no. 1-2; pp. 427 - 455
Main Authors Charpentier, S., Nestoridis, V., Wielonsky, F.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2015
Springer
Subjects
Classical Analysis and ODEs
Functional Analysis
Mathematics
Mathematics and Statistics
Generic property
Universal Taylor series
Padé approximant
30K05
41A21
41A10
generic property
universal Taylor series
Online AccessGet full text
ISSN0025-5874
1432-1823
DOI10.1007/s00209-015-1493-9

Cover

More Information
Summary:We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infinite dimensional linear subspaces of analytic functions in a simply connected domain of the complex plane, containing the origin, whose all non zero elements are made of Padé universal series. We also show how Padé universal series can be built from classical universal series with large Ostrowski-gaps.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-015-1493-9