Hypercyclic Sequences of Differential and Antidifferential Operators

✍ Scribed by Luis Bernal-González

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 150 KB
• Volume: 96
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1998.3237

✦ Synopsis

In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fre chet space of entire functions of several complex variables. Specifically, we generalize in several directions a theorem about hypercyclicity of certain infinite order linear differential operators with constant coefficients and study the corresponding property for certain kinds of ``antidifferential'' operators which are introduced in the paper. In addition, the existence of hypercyclic functions for certain sequences of differential operators with additional properties, for instance, boundedness or with some nonvanishing derivatives, is established.