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Title: Nonabsolutely convergent series (English)
Author: Fraňková, Dana
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 116
Issue: 3
Year: 1991
Pages: 248-267
Summary lang: English
Category: math
Summary: Assume that for any $t$ from an interval $[a,b]$ a real number $u(t)$ is given. Summarizing all these numbers $u(t)$ is no problem in case of an absolutely convergent series $\sum_{t\in[a,b]}u(t)$. The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral. (English)
Keyword: nonabsolutely convergent series
Keyword: generalized Perron integral
MSC: 26A39
MSC: 26A42
MSC: 40A05
idZBL: Zbl 0742.40002
idMR: MR1126447
DOI: 10.21136/MB.1991.126175
Date available: 2009-09-24T20:45:33Z
Last updated: 2020-07-29
Stable URL:
Reference: [K] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a pararaeter.Czech. Math. Ј. 7 (82) (1957), 418-449.
Reference: [S] Š. Schwabik: Generalized differential equations: Fundamental results.Rozpгavy ČSAV (95) (1985), No. 6. Zbl 0594.34002


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