3 papers
math.DS2025
Classification of Principle 3D Slices of Filled-in Julia Sets in Multicomplex Spaces
Quentin Charles, Pierre-Olivier Parisé
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are…
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…
math.RA2022
Involutions of Bicomplex Numbers
Pierre-Olivier Parisé
An involution of a real commutative algebra is a real-linear homomorphism such that . We show that there are six involutions of the alg…