The Theory of H(b) Spaces: Volume 2

by Emmanuel Fricain, Javad Mashreghi

Overview

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

Product Details

ISBN-13:	9781107027787
Publisher:	Cambridge University Press
Publication date:	10/20/2016
Series:	New Mathematical Monographs , #21
Pages:	640
Product dimensions:	6.22(w) x 9.29(h) x 1.77(d)

About the Author

Emmanuel Fricain is Professor of Mathematics at Laboratoire Paul Painlevé, Université Lille 1, France. Part of his research focuses on the interaction between complex analysis and operator theory, which is the main content of this book. He has a wealth of experience teaching numerous graduate courses on different aspects of analytic Hilbert spaces, and he has published several papers on H(b) spaces in high-quality journals, making him a world specialist in this subject.

Javad Mashreghi is a Professor of Mathematics at the Université Laval, Québec, Canada, where he has been selected Star Professor of the Year seven times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis. He is the author of several mathematical textbooks, monographs and research articles. He won the G. de B. Robinson Award, the publication prize of the Canadian Mathematical Society, in 2004.

Table of Contents

Preface; 16. The spaces M(A) and H(A); 17. Hilbert spaces inside H2; 18. The structure of H(b) and H(b̅ ); 19. Geometric representation of H(b) spaces; 20. Representation theorems for H(b) and H(b̅); 21. Angular derivatives of H(b) functions; 22. Bernstein-type inequalities; 23. H(b) spaces generated by a nonextreme symbol b; 24. Operators on H(b) spaces with b nonextreme; 25. H(b) spaces generated by an extreme symbol b; 26. Operators on H(b) spaces with b extreme; 27. Inclusion between two H(b) spaces; 28. Topics regarding inclusions M(a) ⊂ H(b̅) ⊂ H(b); 29. Rigid functions and strongly exposed points of H1; 30. Nearly invariant subspaces and kernels of Toeplitz operators; 31. Geometric properties of sequences of reproducing kernels; References; Symbols index; Index.

Editorial Reviews

'The monograph contains numerous references to original papers, as well as numerous exercises. This monograph may be strongly recommended as a good introduction to this interesting and intensively developing branch of analysis …' Vladimir S. Pilidi, Zentralblatt MATH

'As with Volume 1, chapter notes outline historical development, and an extensive bibliography cites substantial work done in the area since 2000.' Joseph D. Lakey, MathSciNet

‘… designed for a person who wants to learn the theory of these spaces and understand the state of the art in the area. All major results are included. In some situations the original proofs are provided, while in other cases they provide the 'better' proofs that have become available since. The books are designed to be accessible to both experts and newcomers to the area. Comments at the end of each section are very helpful, and the numerous exercises were clearly chosen to help master some of the techniques and tools used … In sum, these are excellent books that are bound to become standard references for the theory of H(b) spaces.’ Bulletin of the American Mathematical Society

From the Publisher