We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
We study a class of nonlinear difference equations admitting a -Gevrey formal power series solution which, in general, is not - (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called quasi-functions, we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an accelero-sum of the formal power series.
This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.