In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.

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.

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.