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Softcover ISBN:  9781470410452 
Product Code:  CONM/638 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470423414 
Product Code:  CONM/638.E 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470410452 
eBook ISBN:  9781470423414 
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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 shiftinvariant subspaces.
This book is copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate students and research mathematicians interested in operator theory and function spaces.

Table of Contents

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 extensioninterpolation on arbitrary sets in one dimension

Emmanuel Fricain, Javad Mashreghi and Daniel Seco — Cyclicity in nonextreme de BrangesRovnyak 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


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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 shiftinvariant subspaces.
This book is copublished 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 extensioninterpolation on arbitrary sets in one dimension

Emmanuel Fricain, Javad Mashreghi and Daniel Seco — Cyclicity in nonextreme de BrangesRovnyak 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