Dynamical properties of weighted translation operators on the Schwartz space $$\mathcal {S}(\mathbb {R})$$S(R)
Dynamical properties of weighted translation operators on the Schwartz space $$\mathcal {S}(\mathbb {R})$$S(R)
In this paper we investigate the dynamical properties of weighted translation operators acting on the Schwartz space $$\mathcal {S}(\mathbb {R})$$ of rapidly decreasing functions, i.e., operators of the form $${T_w}:{\mathcal {S}(\mathbb {R})}\rightarrow {\mathcal {S}(\mathbb {R})},~f(\cdot )\mapsto w(\cdot )f(\cdot +1)$$. We characterize when those operators are hypercyclic, weakly mixing, mixing and …