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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.
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, William T. Ross, Stephan Ramon Garcia, Daniel E. Poore
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, William T. Ross, Stephan Ramon Garcia, Daniel E. Poore
Department of Math & Statistics Faculty Publications
Unlike Toeplitz operators on H2, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension < 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.
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.