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

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Perala, A., Virtanen, J. A. and Wolf, L. (2013) A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators. Concrete Operators, 1 (1). pp. 28-36. ISSN 2299-3282

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To link to this item DOI: 10.2478/conop-2012-0004

Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:34007
Uncontrolled Keywords:Riemann-Hilbert problems; Hardy spaces; Toeplitz operators; Fredholm properties; eigenvalues
Publisher:Versita
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