Almost periodic sequences and functions with given values
Archivum Mathematicum (2011)
- Volume: 047, Issue: 1, page 1-16
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topVeselý, Michal. "Almost periodic sequences and functions with given values." Archivum Mathematicum 047.1 (2011): 1-16. <http://eudml.org/doc/116529>.
@article{Veselý2011,
abstract = {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 $k$.},
author = {Veselý, Michal},
journal = {Archivum Mathematicum},
keywords = {almost periodic functions; almost periodic sequences; almost periodicity in metric spaces; almost periodic function; almost periodic sequence; almost periodicity in metric space},
language = {eng},
number = {1},
pages = {1-16},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Almost periodic sequences and functions with given values},
url = {http://eudml.org/doc/116529},
volume = {047},
year = {2011},
}
TY - JOUR
AU - Veselý, Michal
TI - Almost periodic sequences and functions with given values
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 1
SP - 1
EP - 16
AB - 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 $k$.
LA - eng
KW - almost periodic functions; almost periodic sequences; almost periodicity in metric spaces; almost periodic function; almost periodic sequence; almost periodicity in metric space
UR - http://eudml.org/doc/116529
ER -
References
top- Bede, B., Gal, S. G., 10.1016/j.fss.2003.08.004, Fuzzy Sets and Systems 147 (3) (2004), 385–403. (2004) Zbl1053.42015MR2100833DOI10.1016/j.fss.2003.08.004
- Corduneanu, C., Almost Periodic Functions, John Wiley and Sons, New York, 1968. (1968) Zbl0175.09101MR0481915
- Flor, P., 10.1007/BF01300676, Monatsh. Math. 67 (1963), 12–17. (1963) Zbl0116.06501MR0168467DOI10.1007/BF01300676
- Jajte, R., On almost-periodic sequences, Colloq. Math. 13 (1964/1965), 265–267. (1964) MR0179761
- Janeczko, S., Zajac, M., Critical points of almost periodic functions, Bull. Polish Acad. Sci. Math. 51 (2003), 107–120. (2003) Zbl1032.57031MR1990965
- Muchnik, A., Semenov, A., Ushakov, M., 10.1016/S0304-3975(02)00847-2, Theoret. Comput. Sci. 304 (2003), 1–33. (2003) Zbl1044.68100MR1992325DOI10.1016/S0304-3975(02)00847-2
- Tornehave, H., On almost periodic movements, Danske Vid. Selsk. Mat.–Fys. Medd. 28 (13) (1954), 1–42. (1954) Zbl0059.07401MR0067481
- Veselý, M., Construction of almost periodic functions with given properties, In preparation.
- Veselý, M., Construction of almost periodic sequences with given properties, Electron. J. Differential Equations 126 (2008), 1–22. (2008) Zbl1165.39014MR2443149
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.