On spectral analysis of self-adjoint Toeplitz operators
Spectral Theory
2022-01-27 v1
Abstract
The paper pursues three objectives. Firstly, we provide an expanded version of 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.
Cite
@article{arxiv.1906.07075,
title = {On spectral analysis of self-adjoint Toeplitz operators},
author = {Alexander V. Sobolev and Dmitri Yafaev},
journal= {arXiv preprint arXiv:1906.07075},
year = {2022}
}
Comments
33 pages