We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that if and only if f(z) is conformally conjugate to .
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on .
We define certain classes of functions associated with functions of bounded variation. Some characterizations of those classes are given.