What question did this study set out to answer?

The aim is to explore unbounded Toeplitz operators with rational matrix symbols and their mathematical properties.

April 10, 2026Open Access

A Toeplitz-like Operator with Rational Matrix Symbol Having Poles Only on the Unit Circle: The Adjoint, Symmetry and Fredholm Characteristics

Key Points

The aim is to explore unbounded Toeplitz operators with rational matrix symbols and their mathematical properties.
Develop state space realization techniques for rational matrix symbols.
Analyze the action, kernel, and range of unbounded Toeplitz operators.
Examine the adjoint operator properties and conditions for symmetry.
Determine Fredholm characteristics of the operators.
Concrete results on the action, kernel, and range of the Toeplitz operators were obtained.
Identified conditions under which the unbounded Toeplitz operators are symmetric.
Established when these operators have a selfadjoint extension.

Abstract

Abstract In this paper we continue our investigation of unbounded Toeplitz operators whose symbols are rational matrix valued functions with poles on the unit circle, which was initiated in 16. We further develop state space realization techniques for the symbols of these unbounded Toeplitz operators, and use the techniques to get more concrete results on the action, kernel and range, as well as the adjoint operator. These results are then used to determine Fredholm characteristics, and to determine when the unbounded Toeplitz operators are symmetric and have a selfadjoint extension.

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Authors

G. J. Groenewald

S. ter Horst

J. J. Jaftha

Journals

Integral Equations and Operator Theory

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A Toeplitz-like Operator with Rational Matrix Symbol Having Poles Only on the Unit Circle: The Adjoint, Symmetry and Fredholm Characteristics

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Abstract

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Authors

Journals

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