Transcription of The Riemann-Hilbert method: from Toeplitz …
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The Riemann-Hilbert method: from Toeplitz …
The Riemann-Hilbert method: from Toeplitz operators to black holesMaria Cristina C maraCAMGSD-Instituto Superior T cnicoEncontro de Ci ncia 2017 Lisboa, 3-5 JulhoThe Riemann-Hilbert method: from Toeplitz operators to black holesMaria Cristina C maraWhat is a Riemann-Hilbert problem?Problem: To determine such that =0 inD, continuous onT =2fonT(1) = ++ +2, +analytic inD(|z|<1)(2)Let (z) = +(1/ z),|z|>1 ; analytic inC\closD, (t) = +(t)for|t|=1. +(t) + (t) =f(t),t T += f,onTg += f,onTThe Riemann-Hilbert method: from Toeplitz operators to black holesMaria Cristina C maraWhat is a Riemann-Hilbert problem?Problem: To determine such that =0 inD, continuous onT =2fonT(1) = ++ +2, +analytic inD(|z|<1)(2)Let (z) = +(1/ z),|z|>1 ; analytic inC\closD, (t) = +(t)for|t|=1. +(t) + (t) =f(t),t T += f,onTg += f,onTThe Riemann-Hilbert method: from Toeplitz operators to black holesMaria Cristina C maraWhat is a Riemann-Hilbert problem?
There are no general methods to solve matrix RHP. One has to develop custom-made methods, case by case. Considerable progress has been made in explicit factorisation methods. M. C. Câmara, A. F. dos Santos and P. F. dos Santos: Matrix Riemann-Hilbert
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