Shapiro, Joel H. creator Shapiro, Joel H. text New York : Springer-Verlag ©1993 monographic eng

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xiii, 223 pages : illustrations ; 24 cm. 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. Linear Fractional Prologue -- Littlewood's Theorem -- Compactness: Introduction -- Compactness and Univalence -- The Angular Derivative -- Angular Derivatives and Iteration -- Compactness and Eigenfunctions -- Linear Fractional Cyclicity -- Cyclicity and Models -- Compactness from Models -- Compactness: General Case. / Joel H Shapiro Mathematics Analysis Composition operators Geometrische Funktionentheorie Geometric function theory Operatoren Operatoren 515.7246 SHA 9780387940670 :Technical Bureau India Pvt. Ltd. :E/261, Shastri Nagar Delhi 220330 20220908112616.0