On a theorem of Marcinkiewicz and Zygmund for Taylor series

Universal Taylor series

“…II, p. 178). For works related to the above theorem the reader is referred to [5], [6], [7], [14], [8], [9], [15].…”

“…Power series ^ dnZ 71 having the property that, for every z in a non- investigated in [6], [7]. As it turned out, such series are (C, l)-summable for every z, \z\ = 1, up to a finite set, and they are Taylor developments of 1 oo rational functions of a special form.…”

Partial sums of Taylor series on a circle

“…Further, by a straightforward calculation, one can check that the converses of propositions 8, 11 and theorem 12 also hold (see proposition 9 and [3]). with ab € R. We can arrive to the same characterization using the method of the present paper, as well.…”

“…We prove theorems B and C in §2. The methods of proof are different than the methods in [3]. We use factorization and thus, we deal with the zeros of certain polynomials instead of their coefficients.…”

“…-The cardinality of the set E' in theorem 12 can not be supposed denumerable without any other supplementary hypothesis. This with E = {exp(27^^/2 A; ) : k = 0,1,2,...} and t € R (see also [3]). …”