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<p>In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in Groenewald et al. (J Math Anal Appl 532, Paper no. 127925, 2024) of this class of operators, to study the connection with semi-infinite Toeplitz matrices and to determine the essential spectrum and resolvent set.</p>

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A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: matrix representation and spectral analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月31日

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  • Gilbert J. Groenewald,
  • Sanne ter Horst,
  • Jacob J. Jaftha,
  • André C. M. Ran

摘要

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in Groenewald et al. (J Math Anal Appl 532, Paper no. 127925, 2024) of this class of operators, to study the connection with semi-infinite Toeplitz matrices and to determine the essential spectrum and resolvent set.