Nonabsolutely convergent series
Mathematica Bohemica (1991)
- Volume: 116, Issue: 3, page 248-267
- ISSN: 0862-7959
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topFraňková, Dana. "Nonabsolutely convergent series." Mathematica Bohemica 116.3 (1991): 248-267. <http://eudml.org/doc/29329>.
@article{Fraňková1991,
abstract = {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.},
author = {Fraňková, Dana},
journal = {Mathematica Bohemica},
keywords = {nonabsolutely convergent series; generalized Perron integral; nonabsolutely convergent series; generalized Perron integral},
language = {eng},
number = {3},
pages = {248-267},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonabsolutely convergent series},
url = {http://eudml.org/doc/29329},
volume = {116},
year = {1991},
}
TY - JOUR
AU - Fraňková, Dana
TI - Nonabsolutely convergent series
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 3
SP - 248
EP - 267
AB - 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.
LA - eng
KW - nonabsolutely convergent series; generalized Perron integral; nonabsolutely convergent series; generalized Perron integral
UR - http://eudml.org/doc/29329
ER -
References
top- J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a pararaeter, Czech. Math. Ј. 7 (82) (1957), 418-449. (1957)
- Š. Schwabik, Generalized differential equations: Fundamental results, Rozpгavy ČSAV (95) (1985), No. 6. (1985) Zbl0594.34002
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