Abstract
In a work by Artstein-Avidan and Milman the concept of polarity is generalized from the class of convex bodies to the larger class of convex functions. While the only self-polar convex body is the Euclidean ball, it turns out that there are numerous self-polar convex functions. In this work we give a complete characterization of all rotationally invariant self-polar convex functions on R{double-struck} n.
Original language | English (US) |
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Pages (from-to) | 831-838 |
Number of pages | 8 |
Journal | Bulletin des Sciences Mathematiques |
Volume | 136 |
Issue number | 7 |
DOIs | |
State | Published - Oct 2012 |
Keywords
- Convexity
- Polarity