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

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 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.