Tensor Formats Based on Subspaces are Positively Invariant Sets for Laplacian-Like Dynamical Systems
In this note, we show that the set of tensors with bounded rank are positively invariant sets for linear evolution equations defined by Laplacian-like operators. In consequence, once a trajectory of the system enters to this class of set, it will never leave it again.
KeywordsBanach Space Proper Orthogonal Decomposition Continuous Semigroup Tensor Format Tensor Representation
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