31 research outputs found
Another extension of the disc algebra
We identify the complex plane C with the open unit disc D={z:|z|<1} by the
homeomorphism z --> z/(1+|z|). This leads to a compactification of C,
homeomorphic to the closed unit disc. The Euclidean metric on the closed unit
disc induces a metric d on . We identify all uniform limits of
polynomials on with respect to the metric d. The class of the above
limits is an extension of the disc algebra and it is denoted by .
We study properties of the elements of and topological properties
of the class endowed with its natural topology. The class
is different and, from the geometric point of view, richer than
the class introduced in Nestoridis (2010), Arxiv:1009.5364, on
the basis of the chordal metric.Comment: 14 page
Algebraic genericity of frequently universal harmonic functions on trees
We show that the set of frequently universal harmonic functions on a tree T contains a vector space except 0 which is dense in the space of harmonic functions on T seen as subset of CT. In order to prove this we replace the complex plane C by any separable Fréchet space E and we repeat all the theory. © 2020 Elsevier Inc