Chaos for functions of discrete and continuous weighted shift operators (Q2757011)

For a linear operator \(L\) which is a unilateral or bilateral shift on a weighted sequence space, the characteristic of a function \(f\) holomorphic on the spectrum of \(L\) for which \(f(L)\) is a chaotic operator is given. The definition of chaos in the paper is equivalent, for linear operators, to that given in \textit{R. L. Devaney} [``An introduction to chaotic dynamical systems'' New-York (1989; Zbl 0695.58002)]. Similar results are obtained for polynomials \(Q\) of the generator \(d/dx\) of left translations on weighted \(L^p\) spaces.