Entire Functions of Several Complex Variables

Name: Entire Functions of Several Complex Variables
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642703461
Price: 496.64 RON
Availability: InStock

Autor: Pierre Lelong, Lawrence Gruman

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Legare: Carte broșată

Editura: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Disponibilitate: În depozitul extern

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I - Entire functions of several complex variables constitute an important and original chapter in co...

Informații despre carte

Autor

Pierre Lelong, Lawrence Gruman

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2011

Pagini

272

EAN

9783642703461

ISBN

3642703461

Enbook ID

06994929

Editura

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Greutate

441

Dimensiuni

155 x 235 x 17

Descriere completă

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.

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