the center of distances for some multigeometric series
Classical Analysis and ODEs
2019-07-10 v1
Abstract
Basic properties of the center of distances of a set are investigated. Computation of the center for achievement sets is particularly aimed at. A new sufficient condition for the center of distances of the set of subsums of a fast convergent series to consist of only 0 and the terms of the series is found. A complete description of the center of distances for some particular type of multigeometric series is provided. In particular, the center of distances is the union of all centers of distances of where is the set of all -initial subsums of the discussed multigeometric series satisfying some special requirements. Several open questions are raised.
Cite
@article{arxiv.1907.03800,
title = {the center of distances for some multigeometric series},
author = {Michał Banakiewicz and Artur Bartoszewicz and Franciszek Prus-Wiśniowski},
journal= {arXiv preprint arXiv:1907.03800},
year = {2019}
}