1989
DOI: 10.5802/aif.1184
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Partial sums of Taylor series on a circle

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Cited by 14 publications
(11 citation statements)
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“…II, p. 178). For works related to the above theorem the reader is referred to [5], [6], [7], [14], [8], [9], [15].…”
Section: N=0mentioning
confidence: 99%
See 1 more Smart Citation
“…II, p. 178). For works related to the above theorem the reader is referred to [5], [6], [7], [14], [8], [9], [15].…”
Section: N=0mentioning
confidence: 99%
“…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.…”
mentioning
confidence: 99%
“…Examples suggest that not only the limit points of {σ n (x)} but the partial sums s n (x) themselves lie on L(x), and Katsoprinakis [Kat89] proved a general result in this direction when E is uncountable. A related result by Katsoprinakis and Nestoridis [KN89] also answers a question posed by Kahane. A final result is due to Nestoridis [Ne92] and concerns power series c k z k with lim inf |c k | > 0 and E an infinite subset of the unit circle (see also [NP90]).…”
Section: The Marcinkiewicz Multiplier Theorem and Marcinkiewicz Setsmentioning
confidence: 68%
“…We fix z 6 F -Q and v £ {0, I, ... , m -1}. Let {Xv} be a subsequence of N and t(z) = t(z, v, {Xv}) a complex number, such that (3) limam(Ai,+1)+"_1(z) = i(z).…”
Section: Proof Of Theoremmentioning
confidence: 99%