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arXiv · 1009.5364

An extension of the disc Algebra

Vassilis Nestoridis
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Abstract

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.

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Vassilis Nestoridis. 2010-09-27. An extension of the disc Algebra. https://doi.org/10.1112/blms%2Fbds011

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