The compact set of homogeneous quadratic polynomials in $n$ real variables with modulus bounded by 1 on the unit sphere $S^{n-1}$ is trivially semi-definite representable. The compact set of homogeneous ternary quartics with modulus bounded by 1 on the unit sphere $S^2$ is also semi-definite representable. This suggests that the compact set of homogeneous ternary cubics with modulus bounded by 1 on $S^2$ is semi-definite representable. We deduce an explicit semi-definite representation of this norm ball. More generally, we provide a semi-definite description of the cone of inhomogeneous ternary cubics which are nonnegative on $S^2$.
Inertial-sensor bias estimation from brightness/depth images and based on SO(3)-invariant integro/partial-differential equations on the unit sphere
Improved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets
Efficiently Maximizing a Homogeneous Polynomial over Unit Sphere without Convex Relaxation
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