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math.CV2024
Approximations of Functions With Essential Singularities with Applications to Painlevé's First Transcendent
Nicholas Castillo
In this work we develop an algorithmic procedure for associating a function defined on the Riemann surface of the to given asymptotic data from a function at an essential si…
math.CV2023
On the pointwise existence of Cauchy integrals
Nicholas Castillo, Ovidiu Costin, Kriti Sehgal
The Riemann-Hilbert (RH) approach, whose origins can be traced back to Riemann's PhD thesis, is well known to be far-reaching. It provides a general framework for expressing soluti…