Description
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.
Table of Contents
Preface; Notation; 1. Preliminaries; 2. Inner functions; 3. Hardy spaces; 4. Operators on the Hardy space; 5. Model spaces; 6. Operators between model spaces; 7. Boundary behavior; 8. Conjugation; 9. The compressed shift; 10. The commutant lifting theorem; 11. Clark measures; 12. Riesz bases; 13. Truncated Toeplitz operators; References; Index.
