Chaos for functions of discrete and continuous weighted shift operators

For L equal to the unilateral or bilateral shift on a weighted sequence spa ce, we characterize, in terms of f and the weight function, those f holomor phic on the spectrum of L for which f (L) is a chaotic operator. For B equa l to d/dx, the generator of left translation, on weighted L-p spaces on [0, infinity) or R, we similarly characterize those polynomials Q for which th e differential operator Q(B) generates a chaotic semigroup.