arXiv subjects
Publications and source records attributed to Chung-Chuan Chen.
In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci polynomials, Lucas polynomials, Pell polynomials, Pell-Lucas polynomials, Fermat polynomials, Fermat-Lucas polynomials, and so on.
In this paper, we analyze recurrent $C_{0}$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_{0}$-rigid semigroups of bounded operators and give a structural characterization of them. A characterization of a Li-Yorke chaoticity of the translation semigroup $(T(t))_{t\geq 0}$ on weighted spaces of integrable functions and continuous functions in terms of admissible weight function is given. The recurrent $C_0$-semigroups induced by semiflows are characterized on the spaces of integrable functions and of spaces of continuous functions.
Let $G$ be a locally compact group, $w$ be a weight on $G$ and $Φ$ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^Φ(G)$. In particular, transitivity is equivalent to the blow-up/collapse property in our case. Moreover, the dense set of periodic elements implies transitivity automatically.
Let $G$ be a locally compact group, and let $Φ$ be a Young function. In this paper, we give sufficient and necessary conditions for weighted translation operators on the Orlicz space $L^Φ(G)$ to be chaotic and topologically multiply recurrent. In particular, chaos implies multiple recurrence in our case.
Let $G$ be a locally compact group, and let $Φ$ be a Young function. In this paper, we give a sufficient and necessary condition for weighted translations on the Orlicz space $L^Φ(G)$ to be disjoint topologically transitive. This characterization for disjoint chaos follows from the investigation on disjoint transitivity immediately.