Simple connectivity and linear chaos

 

Joel H. Shapiro

 

Rend. Circ. Mat. Palermo, Ser. II, Suppl. 56 (1998)

 

Abstract: The goal of this paper is to show that, for domains G of the complex plane, simple connectivity can be characterized by the dynamical properties of certain linear differential operators acting on the space of functions holomorphic on G. The operator-theoretic issues that arise here lead to interesting problems, some of them apparently open. The paper is written so as to be accessible to anyone whose background includes the basics of graduate level complex and functional analysis.

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