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.

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 KT 15. Bases of reproducing kernels and interpolation Bibliography Index. AuthorsEmmanuel Fricain, Université Lyon I Emmanuel Fricain is Maître de conférences at the Institut Camille Jordan, Université 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, Université Laval, Québec 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. Related Books Introduction to the Analysis of Normed Linear Spaces Representation Theorems in Hardy Spaces Holomorphic Spaces Linear Analysis An Introductory Course An Introduction to Hilbert Space Elements of Functional Analysis Introduction to the Analysis of Normed Linear Spaces Representation Theorems in Hardy Spaces 123456 PreviousNextrelated journals Proceedings of the Royal Society of Edinburgh, Section: A Mathematics A flagship publication of the Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics… Combinatorics, Probability and Computing Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability… European Journal of Applied Mathematics Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has… Mathematika Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding… Proceedings of the Royal Society of Edinburgh, Section: A Mathematics A flagship publication of the Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics… Combinatorics, Probability and Computing Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability…