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Convex SO(N)×SO(n)-invariant functions and refinements of von Neumann’s inequality
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 71-89.

A function f on M N×n () which is SO(N)×SO(n)-invariant is convex if and only if its restriction to the subspace of diagonal matrices is convex. This results from Von Neumann type inequalities and appeals, in the case where N=n, to the notion of signed singular value.

Une fonction f sur M N×n () qui est SO(N)×SO(n)-invariante est convexe si et seulement si sa restriction au sous-espace des matrices diagonales est convexe. Ceci résulte de variantes de l’inégalité de Von Neumann et fait appel, dans le cas où N=n, à la notion de valeur singulière signée.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1139
Bernard Dacorogna 1; Pierre Maréchal 2

1 EPFL, CH-1015 Lausanne, Switzerland
2 Université Paul Sabatier, Institut de mathématiques, F-31062 Toulouse cedex 9, France
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Bernard Dacorogna; Pierre Maréchal. Convex $\operatorname{SO}(N)\times \operatorname{SO}(n)$-invariant functions and refinements of von Neumann’s inequality. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 71-89. doi : 10.5802/afst.1139. https://afst.centre-mersenne.org/articles/10.5802/afst.1139/

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