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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hayman, W. K. (Walter Kurt)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Academic, 1989.
Colección:L.M.S. monographs ; 20.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Hayman, W. K.  |q (Walter Kurt) 
245 1 0 |a Subharmonic functions.  |n Vol. 2 /  |c W.K. Hayman. 
264 1 |a London :  |b Academic,  |c 1989. 
300 |a 1 online resource (xxv, 590 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a L.M.S. monographs ;  |v 20 
490 1 |a L.M.S. monographs,  |x 0076-0560 ;  |v 20 
504 |a Includes bibliographical references (pages 865-872) and index. 
500 |a Pages also numbered xxv, 285-875. 
520 |a 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 differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications. 
588 0 |a Print version record. 
505 8 |6 880-01  |a 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. 
505 8 |a 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. 
505 8 |a 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. 
650 0 |a Subharmonic functions. 
650 6 |a Fonctions sous-harmoniques.  |0 (CaQQLa)201-0077511 
650 7 |a MATHEMATICS  |x Calculus.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Mathematical Analysis.  |2 bisacsh 
650 7 |a Subharmonic functions  |2 fast  |0 (OCoLC)fst01136442 
776 0 8 |i Print version:  |a Hayman, W.K. (Walter Kurt).  |t Subharmonic functions. Vol. 2  |z 0123348021  |w (OCoLC)294996412 
830 0 |a L.M.S. monographs ;  |v 20. 
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880 0 |6 505-01/(S  |a Front Cover; Subharmonic Functions; Copyright Page; Preface to Volume 2; CORRECTIONS TO VOLUME 1; Acknowledgements; Dedication; Table of Contents; Contents of Volume 1; CHAPTER 6. Maximum and Minimum of Functions Subharmonic in the Plane; 6.0. INTRODUCTION; 6.1. THE RIESZ-HERGLOTZ REPRESENTATION AND THE MILLOUX-SCHMIDT INEQUALITY; 6.2. THE HKN INEQUALITY AND KJELLBERG'S REGULARITY THEOREM; 6.3. FURTHER REGULARITY THEOREMS; 6.4. CASES WHEN C(μ) = 1; A THEOREM OF BEURLING; 6.5. THE WIMAN-VALIRON THEORY; 6.6. HARMONIC FUNCTIONS IN Rm; 6.7. THE MINIMUM OF FUNCTIONS OF SLOW GROWTH.