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Differences, Derivatives, and Decreasing Rearrangements

  • G. F. D. Duff (a1)

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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.

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References

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1. Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities, 2nd ed. (Cambridge, 1952).
2. Kamke, E., Theory of sets (translated; New York, 1950).
3. Riesz, F. and Sz, B.. Nagy, Functional analysis (translated; London, 1955).
4. Titchmarsh, E. C., Theory of functions, 2nd ed. (Oxford, 1939).
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Differences, Derivatives, and Decreasing Rearrangements

  • G. F. D. Duff (a1)

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