Geodesic
An Inductive Rearrangement Theorem
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 184-188

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

In [2, Theorem 3.2, p. 429] and [3, Theorem 2.1, p. 155], the author established two induction theorems which gave rise to a series of fundamental results in spectral and rearrangement inequalities. In particular, the classical inequalities of Hardy-Littlewood-Pólya [4, Theorem 108, p. 89] and Pólya [6] were derived and conditions for equalities obtained (see [2, Theorem 3.8, p. 433] and [3, Theorem 2.6, p. 157]). In [5, Theorem 6, p. 651 ; and Theorem 20, p. 569], Fischer and Holbrook also gave alternative conditions for equalities to hold in the aforesaid inequalities. In this paper, we show that the result of Fischer and Holbrook can be proved by induction using an inductive rearrangement theorem which turns out to be a stronger version of the induction theorems given in [2, Theorem 3.2, p. 429] and [3, Theorem 2.1, p. 155]. 
Chong, Kong-Ming. An Inductive Rearrangement Theorem. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 184-188. doi: 10.4153/CJM-1979-019-0
@article{10_4153_CJM_1979_019_0,
     author = {Chong, Kong-Ming},
     title = {An {Inductive} {Rearrangement} {Theorem}},
     journal = {Canadian journal of mathematics},
     pages = {184--188},
     year = {1979},
     volume = {31},
     number = {1},
     doi = {10.4153/CJM-1979-019-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-019-0/}
}
TY  - JOUR
AU  - Chong, Kong-Ming
TI  - An Inductive Rearrangement Theorem
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 184
EP  - 188
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-019-0/
DO  - 10.4153/CJM-1979-019-0
ID  - 10_4153_CJM_1979_019_0
ER  - 
%0 Journal Article
%A Chong, Kong-Ming
%T An Inductive Rearrangement Theorem
%J Canadian journal of mathematics
%D 1979
%P 184-188
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-019-0/
%R 10.4153/CJM-1979-019-0
%F 10_4153_CJM_1979_019_0

[1] 1. Chong, K. M., Some extensions of a theorem of Hardy, Littlewood and Pôlya and their applications, Can. J. Math. 26 (1974), 1321–1340. Google Scholar

[2] 2. Chong, K. M., A general induction theorem for rearrangements of n-tuples, J. Math. Anal. Appl. 53 (1976), 426–437. Google Scholar

[3] 3. Chong, K. M., An induction theorem for rearrangements, Can. J. Math. 28 (1976), 154–160. Google Scholar

[4] 4. Hardy, G. H., Littlewood, J. E. and Pôlya, G., Inequalities (Cambridge, 1959). Google Scholar

[5] 5. Fischer, P. and Holbrook, J. A. R., Matrices doubly stochastic by blocks, Can. J. Math. 29 (1977), 559–577. Google Scholar

[6] 6. Pôlya, G., Remark on WeyVs note: Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci.. 36 (1950), 49–51. Google Scholar

Cité par Sources :