Growth Theory of Subharmonic Functions

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.

Contenu

1. Preface.- 2. Auxiliary information. Subharmonic functions.- 3. Asymptotic behavior of subharmonic functions of finite order.- 4. Structure of the limit sets.- 5. Applications to entire functions.- 6. Application to the completeness of exponential systems in a convex domain and the multiplicator problem.- Notation.- List of terms.- References.