Asymptotic for a Riemann-Hilbert Problem Solution 1

@article{ArcigaAlejandre2013AsymptoticFA,
  title={Asymptotic for a Riemann-Hilbert Problem Solution 1},
  author={Martin P. Arciga-Alejandre and Jorge S{\'a}nchez-Ortiz and M. Taneco-Hern{\'a}ndez},
  journal={International Journal of Mathematical Analysis},
  year={2013},
  volume={7},
  pages={1667-1672}
}
We solve an homogeneous Riemann-Hilbert problem, such that the density does not satisfy the zero index condition. Moreover, we find an asymptotic representation for the solution to this problem. As an application, the problem mentioned above appears in the construction of a Green operator for a linear partial differential equation with Riesz fractional derivative. Also, in order to estimate such operator the asymptotic representation is used. 
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