A Toeplitz-like operator with rational symbol having poles on the unit circle. I. Fredholm properties
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Groenewald, G.J.
Ter Horst, S.
Ran, A.C.M.
Jaftha, J.
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Springer
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Abstract
In this paper a definition is given for an unbounded Toeplitzlike operator with rational symbol which has poles on the unit circle. It is shown that the operator is Fredholm if and only if the symbol has no zeroes on the unit circle, and a formula for the index is given as well. Finally, a matrix representation of the operator is discussed
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Groenewald, G.J. et al. 2018. A Toeplitz-like operator with rational symbol having poles on the unit circle. I. Fredholm properties. (In Bart, H., Ter Horst, S., Ran, A.C.M. & Woerdeman, H.J., eds. Operator theory, analysis and the state space approach: in Honor of Rien Kaashoek). Operator theory: advances and applications, 271:239-268. [https://doi.org/10.1007/978-3-030-04269-1_10]