具有消失系数的Riemann-Hilbert问题及其在Toeplitz算子上的应用

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2013-09-16 DOI:10.2478/conop-2012-0004

A. Perälä, J. Virtanen, L. Wolf

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引用次数: 1

摘要

摘要研究了具有零值连续系数的齐次Riemann-Hilbert问题。在系数沿从原点出发的几条射线有其值的情况下，我们刻画了非平凡解的不存在性。得到了Hardy空间中Toeplitz算子的注入性和特征值存在性的一些结果。

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A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

Abstract We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

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