Entire Functions of Several Complex Variables (Grundlehren der mathematischen Wissenschaften) pdf epub fb2

Entire Functions of Several Complex Variables (Grundlehren der mathematischen Wissenschaften) by Pierre Lelong pdf epub fb2

Entire Functions of Several Complex Variables (Grundlehren der mathematischen Wissenschaften) Author: Pierre Lelong
Title: Entire Functions of Several Complex Variables (Grundlehren der mathematischen Wissenschaften)
ISBN: 3540152962
ISBN13: 978-3540152965
Other Formats: lit lrf azw mbr
Pages: 272 pages
Publisher: Springer; 1 edition (April 11, 1986)
Language: English
Category: Science & Math
Size PDF version: 1868 kb
Size EPUB version: 1680 kb
Subcategory: Mathematics




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.