This is really cool!  I was actually looking for something like Lemma 5.9 
in your preprint, and definitely did not expect to find it on julia-users. 
 Thanks for saving me the time!

On Tuesday, July 7, 2015 at 5:41:36 AM UTC-7, [email protected] 
wrote:
>
> This is to announce the v0.0.1 release of the new package 
> SingularIntegralEquations.jl 
> <https://github.com/ApproxFun/SingularIntegralEquations.jl>
>
> Built on top of the fast linear algebra for function approximation in 
> ApproxFun, this new package solves problems in acoustic scattering 
> (Helmholtz and gravity Helmholtz equations), potential theory (Laplace 
> equation), fracture mechanics, and Riemann--Hilbert problems.
>
> There is a preprint available on the package's readme for algorithmic 
> details.
>
> Joint work with Sheehan Olver.
>

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