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Date: | 2019 |
Abstract: | For any positive decreasing to zero sequence a_n such that Ʃa_n diverges we consider the related series Ʃk_na_n and Ʃj_na_n. Here, k_n and j_n are real sequences such that Ʃk_nє{0,1} and j_nє{-1,1}. We study their convergence and characterize it in terms of the density of 1's in the sequences k_n and j_n. We extend our results to series m_na_n, with Ʃm_nє{-1,0,1} and apply them to study some associated random series. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-555 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Divergent series ; Harmonic series ; Random series ; Signed sums ; Subsums |
Published in: | Communications on pure & applied analysis, Vol. 18, issue 1 (Jan. 2019) , p. 479-492, ISSN 1553-5258 |
Postprint 15 p, 328.9 KB |