عنوان

Entire Functions of Several Complex Variables

(Number (ISBN

3642703445

(Number (ISBN

3642703461

(Number (ISBN

9783642703447

(Number (ISBN

9783642703461

Number

b572924

Title Proper

Entire Functions of Several Complex Variables

General Material Designation

[Book]

First Statement of Responsibility

by Pierre Lelong, Lawrence Gruman.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1986

Series Title

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 282.

Text of Note

1. Measures of Growth --; ʹ1. Preliminaries --; ʹ 2. Subharmonic and Plurisubharmonic Functions --; ʹ3. Norms on?n and Order of Growth --; ʹ4. Minimal Growth: Liouville's Theorem and Generalizations --; ʹ 5. Entire Functions of Finite Order --; ʹ6. Proximate Orders --; ʹ7. Regularizations --; ʹ 8. Indicator of Growth Functions --; ʹ 9. Exceptional Sets for Growth Conditions --; Historical Notes --; 2. Local Metric Properties of Zero Sets and Positive Closed Currents --; ʹ1. Positive Currents --; ʹ2. Exterior Product --; ʹ3. Positive Closed Currents --; ʹ 4. Positive Closed Currents of Degree 1 --; ʹ5. Analytic Varieties and Currents of Integration --; Historical Notes --; 3. The Relationship Between the Growth of an Entire Function and the Growth of its Zero Set --; ʹ1. Positive Closed Currents of Degree 1 Associated with a Positive Divisor --; ʹ 2. Indicators of Growth of Cousin Data in?n --; ʹ3. Canonical Potentials in?m --; ʹ 4. The Canonical Representation of Entire Functions of Finite Order --; ʹ5. Solution of the?

Text of Note

I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.

Differential equations, Partial.

Mathematics.

Class number

Book number

by Pierre Lelong, Lawrence Gruman.

Lawrence Gruman

Pierre Lelong

Electronic name

[Book]

Y