AI 中文总结
本文综述延拓后等价性在Toeplitz算子相关算子中的应用，指出配对算子的关键作用，研究广义Toeplitz算子的可逆性与Fredholm性质，取得仅用有限信息即可完整描述其核的新成果。
AI 中文摘要
本文在Toeplitz算子、截断Toeplitz算子及进一步的推广（包括对偶截断Toeplitz算子和多带截断Toeplitz算子）的背景下，综述延拓后等价性这一主题。配对算子在此被证明起关键作用。这些方法研究的性质包括广义Toeplitz算子的可逆性与Fredholm性质，新结果显示仅利用有限信息常可完整描述这类算子的核。
英文摘要
This paper reviews the subject of equivalence after extension in the context of Toeplitz operators, truncated Toeplitz operators, and further generalizations including dual and multiband truncated Toeplitz operators. Paired operators are shown to play a key role here. Properties under investigation by these methods include the invertibility and Fredholm properties of generalized Toeplitz operators, with new results showing how the kernels of such operators can often be fully described given only limited information.
Comments26 pages. In memory of Franciszek Hugon Szafraniec
