Boundary values in range spaces of co-analytic truncated Toeplitz operators
Andreas Hartmann,William T. Ross +1 more
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In this paper, the authors investigated the non-tangential boundary values of the functions of the backward shift invariant subspace after having applied a co-analytic (truncated) Toeplitz operator.Abstract:
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function de ning 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 shift invariant subspace after having applied a co-analytic (truncated) Toeplitz operator. There appears to be a smoothing effect.read more
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Book ChapterDOI
Recent Progress on Truncated Toeplitz Operators
TL;DR: A survey on the emerging theory of truncated Toeplitz operators can be found in this article, where a brief introduction to the subject is given and many recent developments in the field since Sarason's seminal paper are discussed.
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The Theory of H(b) Spaces
Emmanuel Fricain,Javad Mashreghi +1 more
TL;DR: The theory of H(b) spaces is defined as a collection of analytic functions which are in the image of an operator as discussed by the authors, which is a branch of mathematics that bridges complex analysis and operator theory.
Journal ArticleDOI
Range Spaces of Co-Analytic Toeplitz Operators
TL;DR: In this paper, the authors consider a co-analytic Toeplitz operator on the Hardy space, where the kernel is a model space (backward shift invariant subspace) and discuss the non-tangential boundary behavior in these range spaces.
Journal ArticleDOI
Reducing Subspaces of the Dual Truncated Toeplitz Operator
TL;DR: In this paper, the authors define the dual truncated Toeplitz operators and give some basic properties of them, in particular, spectrum and reducing subspaces of some special DTO operator.
Journal ArticleDOI
Range Spaces of Co-analytic Toeplitz Operators
TL;DR: In this article, the authors discuss the range spaces of Toeplitz operators with co-analytic symbols, focusing on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
References
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Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
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Generalized interpolation in
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Operators, Functions, and Systems: An Easy Reading
TL;DR: In this article, the authors present a companion volume, Operators, Functions, and Systems: An Easy Reading, which combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinite-dimensional system theory and signal processing.
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TL;DR: Hilbert Spaces Inside Hilbert Spaces as discussed by the authors, Cauchy Integral Representations, and Extreme Points are used to represent the Hilbert space inside Hilbert spaces. But they do not consider the inner Hilbert space.