Power-series summability methods in de Branges-Rovnyak spaces
Functional Analysis
2021-09-07 v2 Complex Variables
Abstract
We show that there exists a de Branges-Rovnyak space on the unit disk containing a function with the following property: even though can be approximated by polynomials in , neither the Taylor partial sums of nor their Ces\`aro, Abel, Borel or logarithmic means converge to in . A key tool is a new abstract result showing that, if one regular summability method includes another for scalar sequences, then it automatically does so for certain Banach-space-valued sequences too.
Cite
@article{arxiv.2103.06631,
title = {Power-series summability methods in de Branges-Rovnyak spaces},
author = {Javad Mashreghi and Pierre-Olivier Parisé and Thomas Ransford},
journal= {arXiv preprint arXiv:2103.06631},
year = {2021}
}