Invariant Subspaces of the Shift Operator
Will be published approx. on 30. June 2015
Book
Paperback/Softback
317 pages
978-1-4704-1045-2 (ISBN)
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 Mathematiques, Universite de Montreal, Montreal, 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.
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
464 gr
ISBN-13
978-1-4704-1045-2 (9781470410452)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Javad Mashreghi, Laval University, Quebec, Canada.
Emmanuel Fricain, Universite Lille 1, Villeneuve d'Ascq, France.
William Ross, University of Richmond, VA.
Emmanuel Fricain, Universite Lille 1, Villeneuve d'Ascq, France.
William Ross, University of Richmond, VA.
Content
Approximation numbers of composition operators on a Hilbert space of Dirichlet series by H. Queffelec
A short introduction to de Branges-Rovnyak spaces by D. Timotin
Asymptotic Bohr radius for the polynomials in one complex variable by C. Chu
A survey on preservers of spectra and local spectra by A. Bourhim and J. Mashreghi
Commutants of finite Blaschke product multiplication operators by C. C. Cowen and R. G. Wahl
Complex approximation and extension-interpolation on arbitrary sets in one dimension by P. M. Gauthier
Cyclicity in non-extreme de Branges-Rovnyak spaces by E. Fricain, J. Mashreghi, and D. Seco
Integral representations of the derivatives in $\mathcal{H}(b)$ spaces by E. Fricain and J. Mashreghi
Interpolation and moment in weighted Hardy spaces by A. Boivin and C. Zhu
Model spaces: A survey by S. R. Garcia and W. T. Ross
Note on a Julia operator related to model spaces by D. Timotin
Selected problems in classical function theory by C. Beneteau and D. Khavinson
The linear bound for Haar multiplier paraproducts by K. Bickel, E. T. Sawyer, and B. D. Wick
Transitivity and bundle shifts by R. G. Douglas and A. Xu
Weak $H^1$, the real and complex case by V. V. Andreev and J. A. Cima
A short introduction to de Branges-Rovnyak spaces by D. Timotin
Asymptotic Bohr radius for the polynomials in one complex variable by C. Chu
A survey on preservers of spectra and local spectra by A. Bourhim and J. Mashreghi
Commutants of finite Blaschke product multiplication operators by C. C. Cowen and R. G. Wahl
Complex approximation and extension-interpolation on arbitrary sets in one dimension by P. M. Gauthier
Cyclicity in non-extreme de Branges-Rovnyak spaces by E. Fricain, J. Mashreghi, and D. Seco
Integral representations of the derivatives in $\mathcal{H}(b)$ spaces by E. Fricain and J. Mashreghi
Interpolation and moment in weighted Hardy spaces by A. Boivin and C. Zhu
Model spaces: A survey by S. R. Garcia and W. T. Ross
Note on a Julia operator related to model spaces by D. Timotin
Selected problems in classical function theory by C. Beneteau and D. Khavinson
The linear bound for Haar multiplier paraproducts by K. Bickel, E. T. Sawyer, and B. D. Wick
Transitivity and bundle shifts by R. G. Douglas and A. Xu
Weak $H^1$, the real and complex case by V. V. Andreev and J. A. Cima