Two-term spectral asymptotics in linear elasticity on a Riemannian manifold
Abstract
In this note, by explaining two key methods that were employed in Liu-21 and by giving some remarks, we show that the proof of Theorem 1.1 in Liu-21 is a rigorous proof based on theory of strongly continuous semigroups and pseudodifferential operators. All remarks and comments to paper Liu-21, which were given by Matteo Capoferri, Leonid Friedlander, Michael Levitin and Dmitri Vassiliev in CaFrLeVa-22, are incorrect. The so-called "numerical counter-examples" in CaFrLeVa-22 are useless examples for the two-term asymptotics of the counting functions of the elastic eigenvalues. Clearly, the conclusion and the proof of Liu-21 are completely correct.
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