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A common tool in Casimir physics (and many other areas) is the asymptotic(high-frequency) expansion of eigenvalue densities, employed as either input oroutput of calculations of the asymptotic behavior of various Green functions.Here we clarify some fine points and potentially confusing aspects of thesubject. In particular, we show how recent observations of Kolomeisky et al.[Phys. Rev. A 87 (2013) 042519] fit into the established framework of thedistributional asymptotics of spectral functions.

Some Subtleties in the Relationships among Heat Kernel Invariants, Eigenvalue Distributions, and Quantum Vacuum Energy