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Entire Functions of Several Complex Variables

  • Book
  • © 1986

Overview

Authors:
  1. Pierre Lelong

    1. Université Paris VI, Paris Cedex 05, France

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  2. Lawrence Gruman

    1. UER de mathématiques, C.N.R.S., Université de Provence, Marseille, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 282)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
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  2. Measures of Growth

    • Pierre Lelong, Lawrence Gruman
    Pages 1-29

  3. Local Metric Properties of Zero Sets and Positive Closed Currents

    • Pierre Lelong, Lawrence Gruman
    Pages 30-58

  4. The Relationship Between the Growth of an Entire Function and the Growth of its Zero Set

    • Pierre Lelong, Lawrence Gruman
    Pages 59-94

  5. Functions of Regular Growth

    • Pierre Lelong, Lawrence Gruman
    Pages 95-115

  6. Holomorphic Mappings from ℂn to ℂm

    • Pierre Lelong, Lawrence Gruman
    Pages 116-154

  7. Application of Entire Functions in Number Theory

    • Pierre Lelong, Lawrence Gruman
    Pages 155-166

  8. The Indicator of Growth Theorem

    • Pierre Lelong, Lawrence Gruman
    Pages 167-176

  9. Analytic Functionals

    • Pierre Lelong, Lawrence Gruman
    Pages 177-200

  10. Convolution Operators on Linear Spaces of Entire Functions

    • Pierre Lelong, Lawrence Gruman
    Pages 201-229

  11. Back Matter

    Pages 230-272
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Keywords

About this book

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.

Authors and Affiliations

  • Université Paris VI, Paris Cedex 05, France

    Pierre Lelong

  • UER de mathématiques, C.N.R.S., Université de Provence, Marseille, France

    Lawrence Gruman

Bibliographic Information

  • Book Title: Entire Functions of Several Complex Variables

  • Authors: Pierre Lelong, Lawrence Gruman

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-70344-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Softcover ISBN: 978-3-642-70346-1Published: 17 November 2011

  • eBook ISBN: 978-3-642-70344-7Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 272

  • Topics: Several Complex Variables and Analytic Spaces

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