7 citations · 7 across the 4 of their papers we have counts for
4 papers
Universal entire functions that define order isomorphisms of countable real sets
Paul M. Gauthier
In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism, which is the restriction…
Conformal extensions of functions defined on arbitrary subsets of Riemann surfaces
P. M. Gauthier, V. Nestoridis
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two co…
Density of polynomials in classes of functions on products of planar domains
P. M. Gauthier, V. Nestoridis
We give sufficient conditions on planar domains for polynomials to be dense in the algebras A and A-infinity of the product of these domains, endowed with their natural topologies.…
Zero-free polynomial approximation on a chain of Jordan domains
P. M. Gauthier, Greg Knese
On a compact subset of the plane with connected complement, is it possible to uniformly approximate a continuous function, holomorphic and non-vanishing on the interior, with polyn…