Produktdetails
- Grundlehren der mathematischen Wissenschaften
- Verlag: Springer, Berlin
- Seitenzahl: 270
- Englisch
- Gewicht: 520g
- ISBN-13: 9783540152965
- ISBN-10: 3540152962
- Artikelnr.: 09229771
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 Lindelöf.- 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.
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 Lindelöf.- 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.