Journal of Operator Theory

Volume 77, Issue 1, Winter 2017 pp. 3-17.

Common hypercyclic vectors for families of backward shift operators

Authors: N. Tsirivas
Author institution:Department of Mathematics and Applied Mathematics, Univ. of Crete, Panepistimiopolis Voutes, 700-13, Heraklion, Crete, Greece

Summary: We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift. Some of our results are valid in a more general context, in the sense that they apply for a wide class of hypercyclic operators.

DOI: http://dx.doi.org/10.7900/jot.2015jun13.2106
Keywords: backward shift, hypercyclic operator, common hypercyclic vectors, uniform distribution mod $1$

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