Harmonic and Subharmonic Function Theory on the Hyperbolic Ball
Seiten
2016
Cambridge University Press (Verlag)
978-1-107-54148-1 (ISBN)
Cambridge University Press (Verlag)
978-1-107-54148-1 (ISBN)
This detailed and comprehensive treatment is ideal for established researchers in the field as well as graduate students who wish to learn more about harmonic and subharmonic function theory on the hyperbolic ball and upper half-space. The only prerequisites are a standard beginning graduate course in real analysis.
This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.
This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.
Manfred Stoll is Distinguished Professor Emeritus in the Department of Mathematics at the University of South Carolina. His books include Invariant Potential Theory in the Unit Ball of Cn (Cambridge, 1994) and Introduction to Real Analysis (1997).
Preface; 1. Möbius transformations; 2. Möbius self-maps of the unit ball; 3. Invariant Laplacian, gradient and measure; 4. H-harmonic and H-subharmonic functions; 5. The Poisson kernel; 6. Spherical harmonic expansions; 7. Hardy-type spaces; 8. Boundary behavior of Poisson integrals; 9. The Riesz decomposition theorem; 10. Bergman and Dirichlet spaces; References; Index of symbols; Index.
Erscheinungsdatum | 02.07.2016 |
---|---|
Reihe/Serie | London Mathematical Society Lecture Note Series |
Zusatzinfo | Worked examples or Exercises |
Verlagsort | Cambridge |
Sprache | englisch |
Maße | 152 x 228 mm |
Gewicht | 370 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-107-54148-4 / 1107541484 |
ISBN-13 | 978-1-107-54148-1 / 9781107541481 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Band 5: Hydraulik, Stromfadentheorie, Wellentheorie, Gasdynamik
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
59,95 €