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Composition Operators and Classical Function Theory

Joel H. Shapiro

出版	Springer-Verlag, 1993
主題	Mathematics / CalculusMathematics / Functional AnalysisMathematics / Complex Analysis
ISBN	35409406779783540940678
URL	http://books.google.com.hk/books?id=LPcpAQAAMAAJ&hl=&source=gbs_api

註釋

The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma.