5 papers
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…
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…
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…
Kernel-Summability Methods and the Silverman-Toeplitz Theorem
Pierre-Olivier Parisé
We introduce kernel-summability methods in Banach spaces using the vector-valued integrals and prove an analogue of the Silverman-Toeplitz Theorem for regular kernel-summability me…
Classes of Holomorphic Multicomplex-Valued Functions Generated by Elliptic-Admissible Involutions
Nicolas Doyon, Pierre-Olivier Parisé, William Verreault
We classify and count the real-algebra involutions of the multicomplex algebra that map each element of its canonical monomial basis to a signed monomial…