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Subharmonic functions. Vol. 2 /
Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differentia...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Academic,
1989.
|
| Colección: | L.M.S. monographs ;
20. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- CHAPTER 7. Exceptional Sets7.0. INTRODUCTION; 7.1. THIN SETS; 7.2. FUNCTIONS OF SLOW GROWTH IN THE PLANE; 7.3. GEOMETRIC ESTIMATES FOR CAPACITY; 7.4. SOME APPLICATIONS TO FUNCTION THEORY; 7.5. MINIMUM OF FUNCTIONS IN A HALF-PLANE; 7.6. BOUNDARY BEHAVIOUR IN A HALF-PLANE; 7.7. BOUNDARY BEHAVIOUR IN THE UNIT DISK; CHAPTER 8. Tracts and Asymptotic Values of Plane Subharmonic Functions; 8.0. INTRODUCTION; 8.1. THE CARLEMAN-TSUJI-HEINS CONVEXITY FORMULA; 8.2. GROWTH AND IMAGE OF FUNCTIONS IN THE UNIT DISK; 8.3. FUNCTIONS WITH N TRACTS; 8.4. GROWTH ON ASYMPTOTIC PATHS; 8.5. EXTREMAL LENGTH.
- 8.6. CONFORMAL-MAPPING TECHNIQUES8.7. REGULARITY THEOREMS FOR THE TRACTS; 8.8. MINIMUM ON A CURVE FOR FUNCTIONS OF FINITE LOWER ORDER; CHAPTER 9. Baernstein's Star Function and its Applications; 9.0 INTRODUCTION; 9.1. THE FUNDAMENTAL THEOREM ON THE STAR FUNCTION; 9.2. MEANS AND SYMMETRIZATION; 9.3. MAJORIZATION THEOREMS FOR UNIVALENT FUNCTIONS; 9.4. CONFORMAL MAPPING AND THE HYPERBOLIC METRIC; 9.5. SYMMETRIZATION AND THE HYPERBOLIC METRIC; 9.6. P�OLYA PEAKS AND THE LOCAL INDICATOR FOR FUNCTIONS IN THE PLANE; 9.7. APPLICATIONS TO FUNCTIONS IN THE PLANE: PALEY'S CONJECTURE; 9.8. SOME EXAMPLES.
- 9.9. CONCLUSIONCHAPTER 10. Examples of Subharmonic and Regular Functions, and the MacLane-Hornblower Class; 10.0. INTRODUCTION; 10.1. MINIMAL POSITIVE HARMONIC FUNCTIONS; 10.2. FUNCTIONS WITH BOUNDED MINIMUM; 10.3. ASYMPTOTIC PATHS AND THE MACLANE-HORNBLOWER THEORY; 10.4. GROWTH CONDITIONS FOR THE CLASS; 10.5. THE KJELLBERG-KENNEDY-KATIFI APPROXIMATION METHOD; 10.6. APPROXIMATION IN THE UNIT DISK; 10.7. THE EXISTENCE OF THIN COMPONENTS; References; Index.