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Concrete Operators

Ed. by Ross, William / Mashreghi, Javad

Mathematical Citation Quotient (MCQ) 2017: 0.34

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

A. Perälä / J. A. Virtanen / L. Wolf
Published Online: 2013-09-16 | DOI: https://doi.org/10.2478/conop-2012-0004


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.

Keywords: Riemann-Hilbert problems; Hardy spaces; Toeplitz operators; Fredholm properties; eigenvalues

MSC: 35Q15; 45E05; 30E25; 47B35

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About the article

Received: 2013-05-28

Accepted: 2013-08-06

Published Online: 2013-09-16

Citation Information: Concrete Operators, Volume 1, Pages 28–36, ISSN (Online) 2299-3282, DOI: https://doi.org/10.2478/conop-2012-0004.

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©2013 Versita Sp. z o.o.. This content is open access.

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