Dual-Band General Toeplitz Operators
Dual-Band General Toeplitz Operators
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双频带通用 Toeplitz 算子
DOI：
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发表时间：
2020
影响因子：
1.1
通讯作者：
J. Partington
中科院分区：
文献类型：
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作者：
M. Câmara;Ryan O’Loughlin;J. Partington
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with 4×4documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$4 imes 4$$end{document} matrix symbols. We discuss their norm, their kernel, Fredholmness, invertibility and spectral properties in various situations, focusing on the spectral properties of the dual-band shift, which turns out to be considerably complex, leading to new and nontrivial connections with the boundary behaviour of the associated inner function.
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with 4×4documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$4 imes 4$$end{document} matrix symbols. We discuss their norm, their kernel, Fredholmness, invertibility and spectral properties in various situations, focusing on the spectral properties of the dual-band shift, which turns out to be considerably complex, leading to new and nontrivial connections with the boundary behaviour of the associated inner function.