Uniform summability of power series
1972 ◽
Vol 71
(2)
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pp. 335-341
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Keyword(s):
AbstractIt is shown that for the Cesàro means (C, α) with α > - 1, and for a certain class of more general Nörlund means, summability of the series σan implies uniform summability of the series σan zn in a Stolz angle at z = 1.If B is a normal matrix and (B) denotes the series summability field with the usual Banach space topology, then the vectors {ek} (ek = {0,0,..., 1,0,...}) are said to form a Toplitz basis for (B) relative to a method H if H — Σakek = a for each a = {ak}ε(B). It is shown for example that the above relation holds for B = (C,α), α> − 1 , and H = Abel method; also for B = (C,α) and H = (C,β) with 0 ≤ α ≤ β.Applications are made to theorems on summability factors.
1994 ◽
Vol 46
(5)
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pp. 982-994
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Keyword(s):
1936 ◽
Vol s2-40
(1)
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pp. 345-352
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Keyword(s):
1994 ◽
Vol 115
(2)
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pp. 283-290
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Keyword(s):
1981 ◽
Vol 23
(3)
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pp. 395-412
Keyword(s):
1935 ◽
Vol s1-10
(4)
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pp. 248-253
1934 ◽
Vol s2-36
(1)
◽
pp. 516-531
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Keyword(s):
2004 ◽
Vol 21
(2)
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pp. 439-448
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Keyword(s):