Levy-Steinitz theorem and achievement sets of conditionally convergent series on the real plane

DOI10.1016/J.JMAA.2017.10.034zbMath1385.40001arXiv1705.06472OpenAlexW2614560154MaRDI QIDQ1684727

Szymon Głąb, Jacek Marchwicki

Publication date: 12 December 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06472

zbMATH Keywords

sum rangeconditionally convergent seriesachievement setset of subsums

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05)

Related Items (2)

Subsums of conditionally convergent series in finite dimensional spaces ⋮ Convergence Rates of Subseries

Cites Work

• Rearranging series of vectors on a small set
• Achievement sets on the plane -- perturbations of geometric and multigeometric series
• Topological and measure properties of some self-similar sets
• Series in Banach spaces: conditional and unconditional convergence. Transl. from the Russian by Andrei Iacob
• Multigeometric sequences and cantorvals
• Cantorvals and Subsum Sets of Null Sequences
• Achievement Sets of Sequences
• On the range of purely atomic probability measures
• Fractal series
• Dimension Functions for Fractal Sets Associated to Series
• On a paper of Guthrie and Nymann on subsums of infinite series
• Achievement sets of conditionally convergent series
• On the topological structure of the arithmetic sum of two Cantor sets
• The topological structure of the set of subsums of an infinite series
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