PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Eigenvalues and dynamical properties of weighted backward shifts on the space of real analytic functions

Volume 242 / 2018

Paweł Domański, Can Deha Karıksız Studia Mathematica 242 (2018), 57-78 MSC: Primary 47B37, 46E10, 47A16; Secondary 47A10. DOI: 10.4064/sm8739-6-2017 Published online: 11 January 2018


Usually backward shift is neither chaotic nor hypercyclic. We will show that on the space $\mathscr {A}(\varOmega )$ of real analytic functions on a connected set ${\varOmega }\subseteq \mathbb {R}$ with $0\in {\varOmega }$, the backward shift operator is chaotic and sequentially hypercyclic. We give criteria for chaos and for many other dynamical properties for weighted backward shifts on $\mathscr {A}(\varOmega )$. For special classes of them we give full characterizations. We describe the point spectrum and eigenspaces of weighted backward shifts on $\mathscr {A}(\varOmega )$ as above.


  • Paweł DomańskiFaculty of Mathematics
    and Computer Science
    A. Mickiewicz University Poznań
    Umultowska 87
    61-614 Poznań, Poland
  • Can Deha KarıksızDepartment of Natural
    and Mathematical Sciences for Engineering
    Özyeğin University
    Nişantepe Mah. Orman Sok. Çekmeköy
    34794 Istanbul, Turkey

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image