成对核与截断托普利兹算子

arXiv - MATH - Functional Analysis Pub Date : 2024-09-04 DOI:arxiv-2409.02563

M. Cristina Câmara, Jonathan R. Partington

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摘要

本文在单位圆上的勒贝格希尔伯特空间 $L^2$ 及其子空间哈代空间 $H^2$ 的背景下研究成对算子。研究了这类算子的核及其解析投影，它们是托普利兹核的广义。研究详细考虑了这些核之间的包含关系，并将结果应用于描述有限级非对称截断托普利兹算子的核。

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Paired kernels and truncated Toeplitz operators

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Inclusion relations between such kernels are considered in detail, and the results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.

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arXiv - MATH - Functional Analysis

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