Geodesic
Rearrangements that Preserve Rates of Divergence
Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 916-920

Voir la notice de l'article provenant de la source Cambridge University Press

Let Σak be an infinite series of real numbers and let π be a permutation of N, the set of positive integers. The series Σaπ(k) is then called a rearrangement of Σak . A classical theorem of Riemann states that if Σak is a conditionally convergent series and s is any fixed real number (or ± ∞), then there is a permuation π such that Σaπ(k) = s. The problem of determining those permutations that convert any conditionally convergent series into a convergent rearrangement (such permuations are called convergence preserving) has received wide attention (see, for example [6]). Of special interest is a paper by P. A. B. Pleasants [5] in which is shown that the set of convergence preserving permutations do not form a group.In this paper we consider questions similar to those above, but for rearrangements of divergent series of positive terms. We establish some notation before stating the precise problem. 
Johnston, Elgin H. Rearrangements that Preserve Rates of Divergence. Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 916-920. doi: 10.4153/CJM-1982-064-2
@article{10_4153_CJM_1982_064_2,
     author = {Johnston, Elgin H.},
     title = {Rearrangements that {Preserve} {Rates} of {Divergence}},
     journal = {Canadian journal of mathematics},
     pages = {916--920},
     year = {1982},
     volume = {34},
     number = {4},
     doi = {10.4153/CJM-1982-064-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-064-2/}
}
TY  - JOUR
AU  - Johnston, Elgin H.
TI  - Rearrangements that Preserve Rates of Divergence
JO  - Canadian journal of mathematics
PY  - 1982
SP  - 916
EP  - 920
VL  - 34
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-064-2/
DO  - 10.4153/CJM-1982-064-2
ID  - 10_4153_CJM_1982_064_2
ER  - 
%0 Journal Article
%A Johnston, Elgin H.
%T Rearrangements that Preserve Rates of Divergence
%J Canadian journal of mathematics
%D 1982
%P 916-920
%V 34
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-064-2/
%R 10.4153/CJM-1982-064-2
%F 10_4153_CJM_1982_064_2

[1] 1. Diananda, P. H., On rearrangements of series, Proc. Cambridge Philos. Soc. 58 (1962), 158–159. Google Scholar

[2] 2. Diananda, P. H., On rearrangements of Series II, Colloq. Math. 9 (1962), 277–279. Google Scholar

[3] 3. Diananda, P. H., On rearrangements of Series IV, Colloq. Math. 12 (1964), 85–86. Google Scholar

[4] 4. Johnston, E. H., Rearrangements of diverqent series, to appear in Rocky Mountain J. of Math. Google Scholar

[5] 5. P. A. B., Pleasants, Rearrangements that preserve convergence, J. London Math. Soc. 15 (1977), 134–142. Google Scholar

[6] 6. Schaefer, P., Sum-preserving rearrangements of infinite series, Amer. Math. Monthly 88 (1981), 33–40. Google Scholar

[7] 7. Stenberg, W., On rearrangements of infinite series, Nederl. Akad. Wetenesh. Proc. Ser. 23 (1961), 459–475. Google Scholar

Cité par Sources :