The paper claims the Laplacian kernel enables better kernel DMD reconstruction from sparse irregular data and proves Koopman closability, but the proofs have invalid steps and circular reasoning.
Aronszajn, Theory of reproducing kernels , Transactions of the American Mathematical Society, 68 (1950), pp
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Kernel Dynamic Mode Decomposition For Sparse Reconstruction of Closable Koopman Operators
The paper claims the Laplacian kernel enables better kernel DMD reconstruction from sparse irregular data and proves Koopman closability, but the proofs have invalid steps and circular reasoning.