Grundlehren der mathematischen Wissenschaften

Entire Functions of Several Complex Variables

Authors: Lelong, Pierre, Gruman, Lawrence

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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.

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Measures of Growth

    Pages 1-29

    Lelong, Professor Dr. Pierre (et al.)

  • Local Metric Properties of Zero Sets and Positive Closed Currents

    Pages 30-58

    Lelong, Professor Dr. Pierre (et al.)

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

    Pages 59-94

    Lelong, Professor Dr. Pierre (et al.)

  • Functions of Regular Growth

    Pages 95-115

    Lelong, Professor Dr. Pierre (et al.)

  • Holomorphic Mappings from ℂ n to ℂ m

    Pages 116-154

    Lelong, Professor Dr. Pierre (et al.)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-642-70344-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-70346-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Entire Functions of Several Complex Variables
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
282
Copyright
1986
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-70344-7
DOI
10.1007/978-3-642-70344-7
Softcover ISBN
978-3-642-70346-1
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XII, 272
Topics