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Real Complex Functions, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.

Introduction To Model Spaces And Their Operators, William T. Ross, Stephan Ramon Garcia, Javad Mashreghi

Bookshelf

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

C*-Algebras Generated By Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen

Department of Math & Statistics Faculty Publications

We obtain an analogue of Coburn’s description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.

[Introduction To] Generalized Analytic Continuation, William T. Ross, Harold S. Shapiro

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The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are "continuations" of each other? (2) What role do such "continuations" play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series …

[Introduction To] The Backward Shift On The Hardy Space, William T. Ross, Joseph A. Cima

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Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator.

This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces Hp. The characterization of the backward shift …