The Theory of H(b) Spaces: Volume 1

Inbunden, Engelska, 2016

Del 20 i serien New Mathematical Monographs

2 514 kr

Beställningsvara. Skickas inom 11-20 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-05-26
Mått:158 x 236 x 50 mm
Vikt:1 200 g
Format:Inbunden
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:702
Förlag:Cambridge University Press
ISBN:9781107027770

Utforska kategorier

Mer om författaren

Emmanuel Fricain is a Professor in the Laboratoire Paul Painlevé at Université Lille 1. 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, Québec, 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.

Recensioner i media

'This two volume monograph is a compendium of the H(b) spaces that will be of interest to both graduate students and practicing mathematicians interested in function-theoretic operator theory. There are 31 chapters between the two volumes and a detailed bibliography consisting of 766 entries. The first volume is devoted to general function-theoretic operator theory (and indeed is a useful reference in its own right) while the second volume is more specialized and contains an in-depth survey of H(b)H(b) theory and related ideas.' Steve Deckelman, MAA Reviews

Innehållsförteckning

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 KΘ; 15. Bases of reproducing kernels and interpolation; Bibliography; Index.