Entire functions of several complex variables
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Bibliographic Information
Entire functions of several complex variables
(Die Grundlehren der mathematischen Wissenschaften, 282)
Springer-Verlag, c1986
- : us
- : gw
Available at / 90 libraries
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Science and Technology Library, Kyushu University
: gwSER/GMW/K282A068252186002716,
U1/Lel068252186000092 -
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: gwLEL||3||386004814
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Kobe University General Library / Library for Intercultural Studies
: gw410-8-G//282061000093126
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General Library Yamaguchi University
: us410.8/G785/2820086212682,
: gw410.8/G785/2820223038172, 410.8/G785/2820086212682 -
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Note
Bibliography: p. [254]-268
Includes index
Description and Table of Contents
Description
Table of Contents
- 1. Measures of Growth.- 1. Preliminaries.- 2. Subharmonic and Plurisubharmonic Functions.- 3. Norms on ?n and Order of Growth.- 4. Minimal Growth: Liouville's Theorem and Generalizations.- 5. Entire Functions of Finite Order.- 6. Proximate Orders.- 7. Regularizations.- 8. Indicator of Growth Functions.- 9. Exceptional Sets for Growth Conditions.- Historical Notes.- 2. Local Metric Properties of Zero Sets and Positive Closed Currents.- 1. Positive Currents.- 2. Exterior Product.- 3. Positive Closed Currents.- 4. Positive Closed Currents of Degree 1.- 5. Analytic Varieties and Currents of Integration.- Historical Notes.- 3. The Relationship Between the Growth of an Entire Function and the Growth of its Zero Set.- 1. Positive Closed Currents of Degree 1 Associated with a Positive Divisor.- 2. Indicators of Growth of Cousin Data in ?n.- 3. Canonical Potentials in ?m.- 4. The Canonical Representation of Entire Functions of Finite Order.- 5. Solution of the ? $$\bar \partial$$ Equation.- 6. The Case of a Cousin Data.- 7. Slowly Increasing Cousin Data: the Genus q = 0
- the Algebraic Case.- 8. The Case of Integral Order: Extension of a Theorem of Lindelof.- 9. Trace of a Cousin Data on Complex Lines.- 10. The Case of a Cousin Data of Infinite Order.- Historical Notes.- 4. Functions of Regular Growth.- 1. General Properties of Functions of Regular growth.- 2. Distribution of the Zeros of Functions of Regular Growth.- Historical Notes.- 5. Holomorphic Mappings from ?n to ?m.- 1. Representation of an Analytic Variety Y in ?n as F-1(0).- 2. Local Potentials and the Defect of Plurisubharmonicity.- 3. Global Potentials.- 4. Construction of a System F of Entire Functions such that Y=F-1(0).- 5. The Case of Slow Growth.- 6. The Algebraic Case.- 7. The Pseudo Algebraic Case.- 8. Counterexamples to Uniform Upper Bounds.- 9. An Upper Bound for the Area of F-1(a) for a Holomorphic Map.- 10. Upper and Lower Bounds for the Trace of an Analytic Variety on Complex Planes.- Historical Notes.- 6. Application of Entire Functions in Number Theory.- 1. Preliminaries from Number Theory.- 2. A Schwarz Lemma.- 3. Statement and Proof of the Main Theorem.- Historical Notes.- 7. The Indicator of Growth Theorem.- Historical Notes.- 8. Analytic Functionals.- 1. Convex Sets and the Fourier-Borel Transform.- 2. The Projective Indicator.- 3. The Projective Laplace Transform.- 4. The Case of M a Complex Submanifold of ?n.- 5. The Generalized Laplace Transform and Indicator Function.- 6. Support for Analytic Functionals.- 7. Unique Supports for Domains in ?n.- 8. Unique Convex Supports.- Historical Notes.- 9. Convolution Operators on Linear Spaces of Entire Functions.- 1. Linear Topological Spaces of Entire Functions.- 2. Theorems of Division.- 3. Applications of Convolution Operators in the Spaces Ep?(r)and Eo.- 4. Supplementary Results for Proximate Orders with ?>1.- 5. The Case ?=1.- 6. More on Functions of Order Less than One.- 7. Convolution Operators in ?n.- Historical Notes.- Appendix I. Subharmonic and Plurisubharmonic Functions.- Appendix II. The Existence of Proximate Orders.
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