Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

ISBN-13: 9781107541481 / Angielski / Miękka / 2016 / 230 str.

Manfred Stoll

Opis

A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.

Recenzje

'The author gives a comprehensive treatment of invariant potential theory. The exposition is clear and elementary. This book is recommended to graduate students and researchers interested in this field. It is a very good addition to the mathematical literature.' Hiroaki Aikawa, MathSciNet

Spis treści

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.