On conditionally convergent series
Анотація
The most interesting result of the paper is that for any two complemen- tary subsets A and B of the set of positive odd integers there exists such a sequence {ak}∞k=1 Ì [-1,1] that"mÎ A:the series is convergent and
"mÎ B:the series is divergent.
Using the map as a substitute of the power function, one can prove similar results for vectors and positive not necessarily integer exponents l.
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Logvinenko, V. On conditionally convergent series. Мат. физ. анал. геом. 2004, 11, 470-483.
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