The Theory of H(b) Spaces

Volume 1 + Volume 2

AUTHORS:Emmanuel Fricain, Université de Lille IJavad Mashreghi, Université Laval, Québec





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.

• Covers all of the material required to understand the theory and its foundations
• Suitable as a textbook for graduate courses
• Both volumes together contain over 400 exercises to test students' grasp of the material