# Holomorphic Functions of Finite Order in Several Complex Variables

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*Wilhelm Stoll*

A co-publication of the AMS and CBMS

In this expository paper one fundamental aspect of the theory, the construction of holomorphic functions with growth estimates to given zero sets, was selected as the central topic of the survey. In addition to two main theorems of value distribution are stated for a meromorphic map of a hermitian vector space into a complex projective space because of the fundamental importance of these theorems.

#### Reviews & Endorsements

This monograph contains a survey of some recent research in the theory of distribution of values of holomorphic and meromorphic functions in \({\mathbf C}^n\). The main attention is on the question of the existence and integral representation of a function with given divisor.

-- L. I. Ronkin, Mathematical Reviews

#### Table of Contents

# Table of Contents

## Holomorphic Functions of Finite Order in Several Complex Variables

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface ix10 free
- 1. Review of some basic results in one variable 112 free
- 2. Hermitian vector space 415
- 3. Analytic chains and divisors 819
- 4. The two main theorems 1627
- 5. The Jensen-Poisson formula. Canonical functions 2233
- 6. Functions of finite order 2839
- 7. Theta functions 3445
- 8. Functions of finite λ-type 3849
- 9. Functions of finite order on the unit ball 4152
- 10. Functions of finite order on polydiscs 4556
- 11. Entire functions for analytic sets 6980
- References 7788
- Index 8293 free
- Back Cover Back Cover197