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Open Access Published by De Gruyter Open Access September 16, 2013

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

  • A. Perälä EMAIL logo , J. A. Virtanen and L. Wolf
From the journal Concrete 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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Received: 2013-05-28
Accepted: 2013-08-06
Published Online: 2013-09-16

©2013 Versita Sp. z o.o.

This content is open access.

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