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Solution de la question 361

Marechal — 1857

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Convex $SO (N) \times SO (n)$ -invariant functions and refinements of von Neumann’s inequality

Bernard Dacorogna; Pierre Maréchal — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

A function $f$ on $M_{N \times n} (ℝ)$ which is $SO (N) \times SO (n)$ -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 .

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Solution de la question 361

Convex SO ( N ) × SO ( n ) -invariant functions and refinements of von Neumann’s inequality

Convex $SO (N) \times SO (n)$ -invariant functions and refinements of von Neumann’s inequality