Author | Lelong, Pierre. author |
---|---|
Title | Entire Functions of Several Complex Variables [electronic resource] / by Pierre Lelong, Lawrence Gruman |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-70344-7 |
Descript | XII, 272 p. online resource |
1. Measures of Growth -- ยง1. Preliminaries -- ยง 2. Subharmonic and Plurisubharmonic Functions -- ยง3. Norms on ?n and Order of Growth -- ยง4. Minimal Growth: Liouvilleโs Theorem and Generalizations -- ยง 5. Entire Functions of Finite Order -- ยง6. Proximate Orders -- ยง7. Regularizations -- ยง 8. Indicator of Growth Functions -- ยง 9. Exceptional Sets for Growth Conditions -- Historical Notes -- 2. Local Metric Properties of Zero Sets and Positive Closed Currents -- ยง1. Positive Currents -- ยง2. Exterior Product -- ยง3. Positive Closed Currents -- ยง 4. Positive Closed Currents of Degree 1 -- ยง5. 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 -- ยง1. Positive Closed Currents of Degree 1 Associated with a Positive Divisor -- ยง 2. Indicators of Growth of Cousin Data in ?n -- ยง3. Canonical Potentials in ?m -- ยง 4. The Canonical Representation of Entire Functions of Finite Order -- ยง5. Solution of the ? $$\bar \partial$$ Equation -- ยง 6. The Case of a Cousin Data -- ยง7. Slowly Increasing Cousin Data: the Genus q = 0; the Algebraic Case -- ยง8. The Case of Integral Order: Extension of a Theorem of Lindelรถf -- ยง 9. Trace of a Cousin Data on Complex Lines -- ยง 10. The Case of a Cousin Data of Infinite Order -- Historical Notes -- 4. Functions of Regular Growth -- ยง 1. General Properties of Functions of Regular growth -- ยง2. Distribution of the Zeros of Functions of Regular Growth -- Historical Notes -- 5. Holomorphic Mappings from ?n to ?m -- ยง1. Representation of an Analytic Variety Y in ?n as F-1(0) -- ยง2. Local Potentials and the Defect of Plurisubharmonicity -- ยง3. Global Potentials -- ยง 4. Construction of a System F of Entire Functions such that Y=F-1(0) -- ยง5. The Case of Slow Growth -- ยง6. The Algebraic Case -- ยง7. The Pseudo Algebraic Case -- ยง8. Counterexamples to Uniform Upper Bounds -- ยง9. An Upper Bound for the Area of F-1(a) for a Holomorphic Map -- ยง 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 -- ยง1. Preliminaries from Number Theory -- ยง2. A Schwarz Lemma -- ยง3. Statement and Proof of the Main Theorem -- Historical Notes -- 7. The Indicator of Growth Theorem -- Historical Notes -- 8. Analytic Functionals -- ยง1. Convex Sets and the Fourier-Borel Transform -- ยง2. The Projective Indicator -- ยง3. The Projective Laplace Transform -- ยง4. The Case of M a Complex Submanifold of ?n -- ยง5. The Generalized Laplace Transform and Indicator Function -- ยง6. Support for Analytic Functionals -- ยง7. Unique Supports for Domains in ?n -- ยง8. Unique Convex Supports -- Historical Notes -- 9. Convolution Operators on Linear Spaces of Entire Functions -- ยง1. Linear Topological Spaces of Entire Functions -- ยง 2. Theorems of Division -- ยง3. Applications of Convolution Operators in the Spaces Ep?(r)and Eo -- ยง4. Supplementary Results for Proximate Orders with ?>1 -- ยง5. The Case ?=1 -- ยง 6. More on Functions of Order Less than One -- ยง 7. Convolution Operators in ?n -- Historical Notes -- Appendix I. Subharmonic and Plurisubharmonic Functions -- Appendix II. The Existence of Proximate Orders