Banach Spaces of Universal Taylor Series in the Disc Algebra

Abstract

Abstract. It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies that, for many small subsets E of the unit circle T, the restrictions to T of the partial sums of its Taylor series at the origin approximate any prescribed function on E. Moreover, it is shown that such sets necessarily have to be small in terms of porosity.Mathematics Subject Classification (2010). Primary 47A16; Secondary 15A03, 40A30, 42A16, 46E10.