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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia
Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper [88] from 2007.
Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Department of Math & Statistics Faculty Publications
The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that for all f∈H2, the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that for all f∈H2. The first type of inequality above was explored with H2 replaced by one of the model spaces (Θ H2)⊥ by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss …
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
Department of Math & Statistics Faculty Publications
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.
In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …
Truncated Toeplitz Operators And Boundary Values In Nearly Invariant Subspaces, William T. Ross, Andreas Hartmann
Truncated Toeplitz Operators And Boundary Values In Nearly Invariant Subspaces, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
We consider truncated Toeplitz operator on nearly invariant subspaces of the Hardy space H2. Of some importance in this context is the boundary behavior of the functions in these spaces which we will discuss in some detail.