Growth Theory of Subharmonic Functions

This book gives an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.

In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables.

The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function.

All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.

Provides a well-organized account of the asymptotic behaviour of subharmonic functions (in n dimensions) with applications to the study of the growth of entire functions of one complex variable Clearly written, at the level of a second year graduate student specializing in analysis, and contains many exercises Presents the application of a new tool, the limit set of entire and subharmonic functions Includes supplementary material: sn.pub/extras

Contenu
Preface.- Auxiliary Information. Subharmonic Functions.- Asymptotic Behavior of Subharmonic Functions of Finite Order.- Structure of Limit Sets.- Applications to Entire Functions.- Application to the Completeness of Exponential Systems in Convex Domains and the Multiplicator Problem.