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On spectral analysis of self-adjoint Toeplitz operators

Sobolev, AV; Yafaev, D; (2020) On spectral analysis of self-adjoint Toeplitz operators. Journal of Operator Theory , 84 (2) pp. 453-485. 10.7900/jot.2019jun19.2244. Green open access

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Abstract

The paper pursues three objectives. First, we provide an expanded version of the spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for instance, our proof of the absolute continuity, relying on a weak version of the limiting absorption principle, is more direct. Secondly, we study in detail Toeplitz operators with finite spectral multiplicity. In particular, we introduce generalized eigenfunctions and investigate their properties. Thirdly, we develop a more detailed spectral analysis for piecewise continuous symbols. This is necessary for construction of scattering theory for Toeplitz operators with such symbols.

Type: Article
Title: On spectral analysis of self-adjoint Toeplitz operators
Open access status: An open access version is available from UCL Discovery
DOI: 10.7900/jot.2019jun19.2244
Publisher version: https://doi.org/10.7900/jot.2019jun19.2244
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: Toeplitz operators, spectral decomposition, discontinuous symbols
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10113145
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