عنوان

Composition operators and classical function theory /

0387940677

3540940677

9780387940670

9783540940678

dltt

Composition operators and classical function theory /

[Book]

Joel H. Shapiro

xiii, 223 pages :

illustrations ;

24 cm

Universitext. Tracts in mathematics

Includes bibliographical references and indexes

0. Linear Fractional Prologue -- 1. Littlewood's Theorem -- 2. Compactness: Introduction -- 3. Compactness and Univalence -- 4. The Angular Derivative -- 5. Angular Derivatives and Iteration -- 6. Compactness and Eigenfunctions -- 7. Linear Fractional Cyclicity -- 8. Cyclicity and Models -- 9. Compactness from Models -- 10. Compactness: General Case

2

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

Composition operators and classical function theory.

Composition operators

Geometric function theory

Shapiro, Joel H

20160712055110.0

[Book]

Y