| Title:
|
Almost periodic sequences and functions with given values (English) |
| Author:
|
Veselý, Michal |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
1-16 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence $\lbrace \psi _k\rbrace _{k \in \mathbb{Z}}$ such that $\lbrace \psi _k; \, k \in \mathbb{Z}\rbrace = X$ and $\psi _k = \psi _{k + l q(k)}$, $l \in \mathbb{Z}$ for all $k$ and some $q(k) \in \mathbb{N}$ which depends on $k$. (English) |
| Keyword:
|
almost periodic functions |
| Keyword:
|
almost periodic sequences |
| Keyword:
|
almost periodicity in metric spaces |
| MSC:
|
11K70 |
| MSC:
|
42A75 |
| idZBL:
|
Zbl 1240.11088 |
| idMR:
|
MR2813542 |
| . |
| Date available:
|
2011-05-23T12:14:06Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141503 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Veselý, M.: Construction of almost periodic functions with given properties.In preparation. |
| Reference:
|
[9] Veselý, M.: Construction of almost periodic sequences with given properties.Electron. J. Differential Equations 126 (2008), 1–22. Zbl 1165.39014, MR 2443149 |
| . |
