| 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:
|
http://hdl.handle.net/10338.dmlcz/126175 |
| . |
| 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 |
| . |
