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

A. Perälä; J. A. Virtanen; L. Wolf

Concrete Operators (2013)

  • Volume: 1, page 28-36
  • ISSN: 2299-3282

Abstract

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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.

How to cite

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A. Perälä, J. A. Virtanen, and L. Wolf. "A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators." Concrete Operators 1 (2013): 28-36. <http://eudml.org/doc/267452>.

@article{A2013,
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.},
author = {A. Perälä, J. A. Virtanen, L. Wolf},
journal = {Concrete Operators},
keywords = {Riemann-Hilbert problems; Hardy spaces; Toeplitz operators; Fredholm properties; eigenvalues},
language = {eng},
pages = {28-36},
title = {A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators},
url = {http://eudml.org/doc/267452},
volume = {1},
year = {2013},
}

TY - JOUR
AU - A. Perälä
AU - J. A. Virtanen
AU - L. Wolf
TI - A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
JO - Concrete Operators
PY - 2013
VL - 1
SP - 28
EP - 36
AB - 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.
LA - eng
KW - Riemann-Hilbert problems; Hardy spaces; Toeplitz operators; Fredholm properties; eigenvalues
UR - http://eudml.org/doc/267452
ER -

References

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  13. [13] E. Shargorodsky, J. F. Toland, Bernoulli free-boundary problems. Mem. Amer. Math. Soc. 196 (2008), no. 914, viii+70 pp. Zbl1167.35001
  14. [14] E. Shargorodsky, J. A. Virtanen, Uniqueness results for the Riemann-Hilbert problem with a vanishing coefficient. Integral Equations Operator Theory 56 (2006), no. 1, 115-127. Zbl1106.35046
  15. [15] J. A. Virtanen, A remark on the Riemann-Hilbert problem with a vanishing coefficient. Math. Nachr. 266 (2004), 85–91. Zbl1055.30034
  16. [16] J. A. Virtanen, Fredholm theory of Toeplitz operators on the Hardy space H1. Bull. London Math. Soc. 38 (2006), no. 1, 143–155. Zbl1092.47032
  17. [17] D. Vukotic, A note on the range of Toeplitz operators. (English summary) Integral Equations Operator Theory 50 (2004), no. 4, 565–567. Zbl1062.47034

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