An Introduction to Operators on the Hardy-Hilbert Space (Paperback)

Ruben A. Martinez-Avendano

ISBN 10: 1441922539 / ISBN 13: 9781441922533

Edité par Springer-Verlag New York Inc., New York, NY, 2010

Paperback. The great mathematician G. H. Hardy told us that Beauty is the ?rst test: there is no permanent place in the world for ugly mathematics (see [24, p. 85]). It is clear why Hardy loved complex analysis: it is a very beautiful partofclassicalmathematics. ThetheoryofHilbertspacesandofoperatorson themisalmostasclassicalandisperhapsasbeautifulascomplexanalysis. The studyoftheHardyHilbertspace(aHilbertspacewhoseelementsareanalytic functions), and of operators on that space, combines these two subjects. The interplay produces a number of extraordinarily elegant results. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. 1. 21 below) and Cauchy integral (Theorem 1. 1. 19) formulas. The fundamental theorem about zeros of fu- tions in the HardyHilbert space (Corollary 2. 4. 10) is the central ingredient of a beautiful proof that every continuous function on [0,1] can be uniformly approximated by polynomials with prime exponents (Corollary 2. 5. 3). The HardyHilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. 2. 12). Conversely, pr- erties of the unilateral shift operator are useful in obtaining results on f- torizations of analytic functions (e. g. , Theorem 2. 3. 4) and on other aspects of analytic functions (e. g. , Theorem 2. 3. 3). The study of Toeplitz operators on the HardyHilbert space is the most natural way of deriving many of the properties of classical Toeplitz mat- ces (e. g. , Theorem 3. 3. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. The fundamental theorem about zeros of fu- tions in the HardyHilbert space (Corollary 2. The HardyHilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9781441922533

Synopsis :

This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.

Présentation de l'éditeur: This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.

Détails bibliographiques

Titre : An Introduction to Operators on the ...
Éditeur : Springer-Verlag New York Inc., New York, NY
Date d'édition : 2010
Reliure : Paperback
Etat : new
Edition : Edition originale