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Invariant Subspaces of the Shift Operator
Edited by: Javad Mashreghi, Laval University, Quebec, Canada, Emmanuel Fricain, Université Lille 1, Villeneuve d'Ascq, France, and William Ross, University of Richmond, VA
A co-publication of the AMS and Centre de Recherches Mathématiques.
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Contemporary Mathematics
2015; 317 pp; softcover
Volume: 638
ISBN-10: 1-4704-1045-1
ISBN-13: 978-1-4704-1045-2
List Price: US$105 Member Price: US$84
Order Code: CONM/638

This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada.

The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces.

These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory.

Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces.

This book is co-published with the Centre de Recherches Mathématiques.