Linear dynamics in reproducing kernel Hilbert spaces

@article{Mundayadan2018LinearDI,
  title={Linear dynamics in reproducing kernel Hilbert spaces},
  author={Aneesh Mundayadan and Jaydeb Sarkar},
  journal={arXiv: Functional Analysis},
  year={2018}
}
Complementing the earlier results on dynamics of unilateral weighted shifts, we obtain a sufficient (but not necessary, with supporting examples) condition for hypercyclicity, mixing and chaos for $M_z^*$, the adjoint of $M_z$, on vector-valued analytic reproducing kernel Hilbert spaces $\mathcal{H}$ in terms of the derivatives of kernel functions on the open unit disc $\mathbb{D}$ in $\mathbb{C}$. Here $M_z$ denotes the multiplication operator by the coordinate function $z$, that is \[ (M_z f… Expand

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