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عنوان
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$S$-orbit of translations on locally compact groups via Orlicz spaces
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نوع پژوهش
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مقاله ارائه شده کنفرانسی
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کلیدواژهها
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Orlicz space, locally compact group, weight, Young function, universal, orbit, translation, convolution, hypercyclic.
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چکیده
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Let $\Phi$ be a Young function and $\omega$ be a weight on a locally compact group $G$. For any $S\subseteq G$, a family of left translations $\{L_s\}_{s\in S}$ on the weighted Orlicz space $L^{\Phi}(G, \omega)$, is defined by $L_s f(t):= f(s^{-1}t)$ for all $t\in G$. It is said to have an \emph{$S$-dense orbit} if there exists a function $f\in L^{\Phi}(G, \omega)$, such that $Orb_S(f)=\{L_s(f): s\in S\}$ is dense in $L^{\Phi}(G, \omega)$. We show that no compact groups $G$ have an $S$-dense orbit in $L^{\Phi}(G, \omega)$. Also $S$-dense orbits may occur only on the infinite dimensional weighted Orlicz spaces $L^{\Phi}(G, \omega)$ with the second countable locally compact groups $G$. Moreover, we give a necessary and sufficient condition for $\{L_s\}_{s\in S}$ to have an $S$-dense orbit in $L^{\Phi}(G, \omega)$.
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پژوهشگران
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محمدرضا عظیمی (نفر اول)، ابراهیم اکبربگلو (نفر دوم)
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