The Theory of H(b) Spaces 2 Volume Hardback Set
Published on 20. October 2016
Book
1342 pages
978-1-107-11941-3 (ISBN)
Description
An H(b) space is defined as a collection of analytic functions which 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. The first volume 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. The second volume 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.
Reviews / Votes
'... 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 SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 5 Halftones, unspecified; 25 Line drawings, unspecified
Dimensions
Height: 237 mm
Width: 160 mm
Thickness: 94 mm
Weight
2300 gr
ISBN-13
978-1-107-11941-3 (9781107119413)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Emmanuel Fricain is Maitre de conferences at the Institut Camille Jordan, Universite Claude Bernard Lyon I. A part of his research focuses on the interaction between complex analysis and operator theory, which is the main matter of this book. He has a long experience of teaching numerous graduate courses on different aspects of analytic Hilbert spaces and 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 Laval University, Quebec, where he has been selected Star Professor of the Year five times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis.
Content
Volume 1: List of figures; Preface; List of symbols; Important conventions; 1. *Normed linear spaces and their operators; 2. Some families of operators; 3. Harmonic functions on the open unit disc; 4. Analytic functions on the open unit disc; 5. The corona problem; 6. Extreme and exposed points; 7. More advanced results in operator theory; 8. The shift operator; 9. Analytic reproducing kernel Hilbert spaces; 10. Bases in Banach spaces; 11. Hankel operators; 12. Toeplitz operators; 13. Cauchy transform and Clark measures; 14. Model subspaces K?; 15. Bases of reproducing kernels and interpolation; Bibliography; Index. Volume 2: Preface; 16. The spaces M(A) and H(A); 17. Hilbert spaces inside H2; 18. The structure of H(b) and H(b? ); 19. Geometric representation of H(b) spaces; 20. Representation theorems for H(b) and H(b?); 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(b?) ? 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.