scholarly journals Addendum: Fourier-Stieltjes series with finitely many distinct coefficients and almost periodic sequences

1968 ◽  
Vol 21 (3) ◽  
pp. 618
Author(s):  
G Goes
2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Zhang ◽  
Bin Jing ◽  
Yingqi Li ◽  
Xiaofeng Fang

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Anh N. Le

<p style='text-indent:20px;'>A set <inline-formula><tex-math id="M1">\begin{document}$ E \subset \mathbb{N} $\end{document}</tex-math></inline-formula> is an interpolation set for nilsequences if every bounded function on <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula> can be extended to a nilsequence on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{N} $\end{document}</tex-math></inline-formula>. Following a theorem of Strzelecki, every lacunary set is an interpolation set for nilsequences. We show that sublacunary sets are not interpolation sets for nilsequences. Here <inline-formula><tex-math id="M4">\begin{document}$ \{r_n: n \in \mathbb{N}\} \subset \mathbb{N} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M5">\begin{document}$ r_1 &lt; r_2 &lt; \ldots $\end{document}</tex-math></inline-formula> is <i>sublacunary</i> if <inline-formula><tex-math id="M6">\begin{document}$ \lim_{n \to \infty} (\log r_n)/n = 0 $\end{document}</tex-math></inline-formula>. Furthermore, we prove that the union of an interpolation set for nilsequences and a finite set is an interpolation set for nilsequences. Lastly, we provide a new class of interpolation sets for Bohr almost periodic sequences, and as a result, obtain a new example of interpolation set for <inline-formula><tex-math id="M7">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-step nilsequences which is not an interpolation set for Bohr almost periodic sequences.</p>


2016 ◽  
Vol 284 (1-2) ◽  
pp. 271-284
Author(s):  
T. Jäger ◽  
A. Passeggi ◽  
S. Štimac

Sign in / Sign up

Export Citation Format

Share Document