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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.
An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin
An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin
Department of Math & Statistics Faculty Publications
Suppose E is a subset of the unit circle T and H∞C L∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zn H∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.
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.
Bad Boundary Behavior In Star Invariant Subspaces Ii, William T. Ross, Andreas Hartmann
Bad Boundary Behavior In Star Invariant Subspaces Ii, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
We continue our study begun in [HR11] concerning the radial growth of functions in the model spaces (IH2)⊥.
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward …
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
A truncated Toeplitz operator Aᵩ : KƟ → KƟ is the compression of a Toeplitz operator Tᵩ : H2 → H2 to a model space KƟ := H2 ⊖ ƟH2. For Ɵ inner, let TƟ denote the set of all bounded truncated Toeplitz operators on KƟ. Our main result is a necessary and sufficient condition on inner functions Ɵ1 and Ɵ2 which guarantees that TƟ1 and TƟ2 are spatially isomorphic. (i.e., UTƟ1 = TƟ2 U for some unitary U : KƟ1 …
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.