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.
Bargmann , On a Hilbert space of analytic functions and an associated integral transform part I , Communications on pure and applied mathematics, 14 (1961), 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.