Subseries and signed series

Research output: Contribution to journalArticleResearch

Abstract

© 2019 American Institute of Mathematical Sciences. All rights reserved. For any positive decreasing to zero sequence an such that an diverges we consider the related series knan and jnan. Here, kn and jn are real sequences such that kn ∈ {0, 1} and jn ∈ {−1, 1}. We study their convergence and characterize it in terms of the density of 1’s in the sequences kn and jn. We extend our results to series mnan, with mn ∈ {−1, 0, 1} and apply them to study some associated random series.
Original languageEnglish
Pages (from-to)479-492
JournalCommunications on Pure and Applied Analysis
Volume18
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Divergent series
  • Harmonic series
  • Random series
  • Signed sums
  • Subsums

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