Entire Functions of Several Complex Variables is popular PDF and ePub book, written by Pierre Lelong in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Entire Functions of Several Complex Variables can be Read Online from any device for your convenience.
Entire Functions of Several Complex Variables Book PDF Summary
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.
Detail Book of Entire Functions of Several Complex Variables PDF
- Author : Pierre Lelong
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642703447
- Genre : Mathematics
- Total Page : 283 pages
- Language : English
- PDF File Size : 17,9 Mb
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