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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

Abstract

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.

Authors

  • 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
    e-mail

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