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- W4206506446 abstract "A new class of continuous valuations on the space of convex functions on $mathbb{R}^n$ is introduced. On smooth convex functions, they are defined for $i=0,dots,n$ by begin{equation*} umapsto int_{mathbb{R}^n} zeta(u(x),x,nabla u(x)),[operatorname{D}^2 u(x)]_i,{rm d} x end{equation*} where $zetain C(mathbb{R}timesmathbb{R}^ntimesmathbb{R}^n)$ and $[operatorname{D}^2 u]_i$ is the $i$th elementary symmetric function of the eigenvalues of the Hessian matrix, $operatorname{D}^2 u$, of $u$. Under suitable assumptions on $zeta$, these valuations are shown to be invariant under translations and rotations on convex and coercive functions." @default.
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- W4206506446 date "2020-01-01" @default.
- W4206506446 modified "2023-09-26" @default.
- W4206506446 title "Hessian valuations" @default.
- W4206506446 doi "https://doi.org/10.1512/iumj.2020.69.7960" @default.
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