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math.CV2025
Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Parisé, Malik Younsi
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…
math.CV2023
On the Divergence of Taylor Series in de Branges-Rovnyak Spaces
Pierre-Olivier Parisé, Thomas Ransford
It is known that there exist functions in certain de Branges--Rovnyak spaces whose Taylor series diverge in norm, even though polynomials are dense in the space. This is often prov…