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Book DetailsContemporary MathematicsCentre de Recherches Mathématiques ProceedingsVolume: 638; 2015; 317 ppMSC: Primary 47; 30; 31; 32
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.
ReadershipGraduate students and research mathematicians interested in operator theory and function spaces.
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Table of Contents
-
Articles
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Hervé Queffélec — Approximation numbers of composition operators on a Hilbert space of Dirichlet series
-
Dan Timotin — A short introduction to de Branges–Rovnyak spaces
-
Cheng Chu — Asymptotic Bohr radius for the polynomials in one complex variable
-
Abdellatif Bourhim and Javad Mashreghi — A survey on preservers of spectra and local spectra
-
Carl C. Cowen and Rebecca G. Wahl — Commutants of finite Blaschke product multiplication operators
-
P. M. Gauthier — Complex approximation and extension-interpolation on arbitrary sets in one dimension
-
Emmanuel Fricain, Javad Mashreghi and Daniel Seco — Cyclicity in non-extreme de Branges-Rovnyak spaces
-
Emmanuel Fricain and Javad Mashreghi — Integral representations of the derivatives in $\mathcal {H}(b)$ spaces
-
André Boivin and Changzhong Zhu — Interpolation and moment in weighted Hardy spaces
-
Stephan Ramon Garcia and William T. Ross — Model spaces: A survey
-
Dan Timotin — Note on a Julia operator related to model spaces
-
Catherine Bénéteau and Dmitry Khavinson — Selected problems in classical function theory
-
Kelly Bickel, Eric T. Sawyer and Brett D. Wick — The linear bound for Haar multiplier paraproducts
-
Ronald G. Douglas and Anjian Xu — Transitivity and bundle shifts
-
Valentin V. Andreev and Joseph A. Cima — Weak $H^1$, the real and complex case
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
Graduate students and research mathematicians interested in operator theory and function spaces.
-
Articles
-
Hervé Queffélec — Approximation numbers of composition operators on a Hilbert space of Dirichlet series
-
Dan Timotin — A short introduction to de Branges–Rovnyak spaces
-
Cheng Chu — Asymptotic Bohr radius for the polynomials in one complex variable
-
Abdellatif Bourhim and Javad Mashreghi — A survey on preservers of spectra and local spectra
-
Carl C. Cowen and Rebecca G. Wahl — Commutants of finite Blaschke product multiplication operators
-
P. M. Gauthier — Complex approximation and extension-interpolation on arbitrary sets in one dimension
-
Emmanuel Fricain, Javad Mashreghi and Daniel Seco — Cyclicity in non-extreme de Branges-Rovnyak spaces
-
Emmanuel Fricain and Javad Mashreghi — Integral representations of the derivatives in $\mathcal {H}(b)$ spaces
-
André Boivin and Changzhong Zhu — Interpolation and moment in weighted Hardy spaces
-
Stephan Ramon Garcia and William T. Ross — Model spaces: A survey
-
Dan Timotin — Note on a Julia operator related to model spaces
-
Catherine Bénéteau and Dmitry Khavinson — Selected problems in classical function theory
-
Kelly Bickel, Eric T. Sawyer and Brett D. Wick — The linear bound for Haar multiplier paraproducts
-
Ronald G. Douglas and Anjian Xu — Transitivity and bundle shifts
-
Valentin V. Andreev and Joseph A. Cima — Weak $H^1$, the real and complex case
