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.
@article{bwmeta1.element.doi-10_2478_conop-2012-0004,
author = {A. Per\"al\"a and J. A. Virtanen and L. Wolf},
title = {A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators},
journal = {Concrete Operators},
volume = {1},
year = {2013},
pages = {28-36},
zbl = {1273.35206},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_conop-2012-0004}
}
A. Perälä; J. A. Virtanen; L. Wolf. A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators. Concrete Operators, Tome 1 (2013) pp. 28-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_conop-2012-0004/
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