arXiv subjects
Publications and source records attributed to Vassilis Nestoridis.
We consider generalizations of classical function spaces by requiring that a holomorphic in $Ω$ function satisfies some property when we approach from $Ω$, not the whole boundary, but only a part of it. These spaces endowed with their natural topology are Fr$é$chet spaces. We prove some generic non-extendability results in such spaces and generic nowhere differentiability on the corresponding part of ${\partialΩ}$.
We identify all uniform limits of polynomials on the closed unit disc with respect to the chordal metric \c{hi} . One such limit is f=oo. The other limits are holomorphic functions f:-->C so that for every ζ in the boundary of unit disc D the limf(z) while z-->ζ exists in C U {oo}. The class of the above functions is denoted by A(D)~. We study properties of the members of A(D)~, as well as, some topological properties of A(D)~ endowed with its natural metric topology. There are several open questions and new directions of investigation.