Linear dynamics in reproducing kernel Hilbert spaces
Article Type
Research Article
Publication Title
Bulletin des Sciences Mathematiques
Abstract
Complementing 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 Mz⁎, the adjoint of Mz, on vector-valued analytic reproducing kernel Hilbert spaces H in terms of the derivatives of kernel functions on the open unit disc D in C. Here Mz denotes the multiplication operator by the coordinate function z, that is (Mzf)(w)=wf(w), for all f∈H and w∈D. We analyze the special case of quasi-scalar reproducing kernel Hilbert spaces. We also present a complete characterization of hypercyclicity of Mz⁎ on tridiagonal reproducing kernel Hilbert spaces and some special classes of vector-valued analytic reproducing kernel Hilbert spaces.
DOI
10.1016/j.bulsci.2019.102826
Publication Date
3-1-2020
Recommended Citation
Mundayadan, Aneesh and Sarkar, Jaydeb, "Linear dynamics in reproducing kernel Hilbert spaces" (2020). Journal Articles. 384.
https://digitalcommons.isical.ac.in/journal-articles/384
Comments
Open Access, Green