The variational sequence describes the Helmholtz conditions for local varia- tionality in terms of the Helmholtz map, which is defined on a factor space. We study a tensor modification of this construction and characterize a unique repre- sentative, which is called the Helmholtz operator. For the first and the second order cases we prove that, up to a multiplicative constant, the Helmholtz operator is the unique natural operator of the type in question.
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