#### Title

Invariant Subspaces of the Shift Operator

#### Files

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#### Description

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.

#### ISBN

9781470410452

#### Publication Date

2015

#### Publisher

American Mathematical Society

#### City

Providence, RI

#### Keywords

invariant subspaces, shift operator, Hardy space, Dirichlet space, de Branges–Rovnyak spaces, function theory

#### School

School of Arts and Sciences

#### Department

Math and Computer Science

#### Disciplines

Computer Sciences | Mathematics

#### Recommended Citation

Mashreghi, Javad, Emmanuel Fricain, William Ross. *Invariant Subspaces of the Shift Operator. *Contemporary Mathematics. 638. Providence, R.I.: American Mathematical Society, 2015.