Concerning normal families and applications to the study of flat regions of entire functions

[摘要] The primary purpose of this paper is the consideration of a theorem concerning regions of flatness of entire functions, and to draw some conclusions that result Immediately from the theorem. The proof of this theorem depends upon certain concepts from the theory of normal families of analytic functions, and the theory of kernels of sequences of analytic functions which tend uniformly to infinity. For this reason, we will occupy ourselves at first. with some of the fundamental ideas from these theories. It will be convenient in this work to define boundedness in a domain as boundedness in each closed region contained in the domain. Similarly, uniform convergence in a domain will be taken to mean uniform convergence in each closed region contained in the domain.

[发布机构] Rice University