The Schwarz Lemma (eBook)

Sean Dineen (Autor)

eBook Download: EPUB

2016
256 Seiten
Dover Publications (Verlag)
978-0-486-81097-3 (ISBN)

Infos

Suitable for advanced undergraduates and graduate students, this self-contained overview covers the classical Schwarz lemma, Poincaré distance on the unit disc, hyperbolic manifolds, holomorphic curvature, and the analytic Radon-Nikodym property. 1989 edition.

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The Schwarz lemma is among the simplest results in complex analysis that capture the rigidity of holomorphic functions. This self-contained volume provides a thorough overview of the subject; it assumes no knowledge of intrinsic metrics and aims for the main results, introducing notation, secondary concepts, and techniques as necessary. Suitable for advanced undergraduates and graduate students of mathematics, the two-part treatment covers basic theory and applications. Starting with an exploration of the subject in terms of holomorphic and subharmonic functions, the treatment proves a Schwarz lemma for plurisubharmonic functions and discusses the basic properties of the Poincaré distance and the Schwarz-Pick systems of pseudodistances. Additional topics include hyperbolic manifolds, special domains, pseudometrics defined using the (complex) Green function, holomorphic curvature, and the algebraic metric of Harris. The second part explores fixed point theorems and the analytic Radon-Nikodym property.

Autor

Sean Dineen is Professor Emeritus of Mathematics at the University College Dublin School of Mathematical Sciences. His other books include Complex Analysis of Infinite Dimensional Spaces, Complex Analysis in Locally Convex Spaces, and Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula.

Inhalt

PART I1. The classical Schwarz lemma2. A Schwarz lemma for plurisubharmonic functions3. The Poincaré distance on the unit disc4. Schwarz-Pick systems of pseudodistances5. Hyperbolic manifolds6. Special domains7. Pseudometrics defined using the (complex) Green function8. Holomorphic curvature9. The algebraic metric of HarrisPART II10. A holomorphic characterization of Banach spaces containing c011. Fixed point theorems12. The analytic Radon-Nikodym propertyReferencesIndex 

Produkt-Details

• Erscheint lt. Verlag: 6.4.2016
• Reihe/Serie: Dover Books on Mathematics
• Zusatzinfo: 8 Figs.
• Sprache: englisch
• Maße: 160 x 160 mm
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: analytic radon-nikodym property. • classical schwarz • Complex • Complex Analysis • Complex VariableTheory • Fixed point theorems • Functional Analysis • Functions • graduate students • Green Function • harris radon nikodym property • holomorphic curvature • Holomorphic Functions • holomporhic curvature • hyperbolic manifolds • intrinsic metrics • Mathematics • mathematics majors and students • mathematics study guide • Nonfiction • proofs • pseudometrics • Schwarz lemma • schwarz pick systems of pseudodistances • science and math • science and math, Subharmonic Functions • special domains • subharmonic functions • textbook companion schwarz lemma theorem • Theorems • the poincare distance
• ISBN-10: 0-486-81097-6 / 0486810976
• ISBN-13: 978-0-486-81097-3 / 9780486810973