  This work considers a super-resolution framework for overcomplete tensor
decomposition. Specifically, we view tensor decomposition as a super-resolution
problem of recovering a sum of Dirac measures on the sphere and solve it by
minimizing a continuous analog of the $\ell_1$ norm on the space of measures.
The optimal value of this optimization defines the tensor nuclear norm. Similar
to the separation condition in the super-resolution problem, by explicitly
constructing a dual certificate, we develop incoherence conditions of the
tensor factors so that they form the unique optimal solution of the continuous
analog of $\ell_1$ norm minimization. Remarkably, the derived incoherence
conditions are satisfied with high probability by random tensor factors
uniformly distributed on the sphere, implying global identifiability of random
tensor factors.
