Subseries and signed series
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

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

DOI: 10.3934/cpaa.2019024

Postprint 15 p, 328.9 KB

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