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Holomorphic Functions of Finite Order in Several Complex Variables

A co-publication of the AMS and CBMS
Available Formats:
Electronic ISBN: 978-1-4704-2381-0
Product Code: CBMS/21.E
List Price: $23.00 Individual Price:$18.40
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Holomorphic Functions of Finite Order in Several Complex Variables
A co-publication of the AMS and CBMS
Available Formats:
 Electronic ISBN: 978-1-4704-2381-0 Product Code: CBMS/21.E
 List Price: $23.00 Individual Price:$18.40
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 211974; 83 pp
MSC: Primary 32;

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.

• Chapters
• 1. Review of some basic results in one variable
• 2. Hermitian vector space
• 3. Analytic chains and divisors
• 4. The two main theorems
• 5. The Jensen-Poisson formula. Canonical functions
• 6. Functions of finite order
• 7. Theta functions
• 8. Functions of finite $\lambda$-type
• 9. Functions of finite order on the unit ball
• 10. Functions of finite order on polydiscs
• 11. Entire functions for analytic sets
• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 211974; 83 pp
MSC: Primary 32;

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.

• Chapters
• 1. Review of some basic results in one variable
• 2. Hermitian vector space
• 3. Analytic chains and divisors
• 4. The two main theorems
• 5. The Jensen-Poisson formula. Canonical functions
• 6. Functions of finite order
• 7. Theta functions
• 8. Functions of finite $\lambda$-type
• 9. Functions of finite order on the unit ball
• 10. Functions of finite order on polydiscs
• 11. Entire functions for analytic sets
• 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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