Differences, Derivatives, and Decreasing Rearrangements
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1153-1178
Voir la notice de l'article provenant de la source Cambridge University Press
The decreasing rearrangement of a finite sequence a 1, a 2, ... , an of real numbers is a second sequence a π(1), a π(2), ... , aπ(n) , where π(l), π(2), ... , π(n) is a permutation of 1, 2, ... , n and (1, p. 260). The kth term of the rearranged sequence will be denoted by . Thus the terms of the rearranged sequence correspond to and are equal to those of the given sequence ak, but are arranged in descending (non-increasing) order.
Duff, G. F. D. Differences, Derivatives, and Decreasing Rearrangements. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1153-1178. doi: 10.4153/CJM-1967-105-0
@article{10_4153_CJM_1967_105_0,
author = {Duff, G. F. D.},
title = {Differences, {Derivatives,} and {Decreasing} {Rearrangements}},
journal = {Canadian journal of mathematics},
pages = {1153--1178},
year = {1967},
volume = {19},
number = {1},
doi = {10.4153/CJM-1967-105-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-105-0/}
}
[1] 1. Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities, 2nd ed. (Cambridge, 1952). Google Scholar
[2] 2. Kamke, E., Theory of sets (translated; New York, 1950). Google Scholar
[3] 3. Riesz, F. and Sz, B.. Nagy, Functional analysis (translated; London, 1955). Google Scholar
[4] 4. Titchmarsh, E. C., Theory of functions, 2nd ed. (Oxford, 1939). Google Scholar
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