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Gottwald, Sebastian (2018): Two-Term Spectral Asymptotics for the Dirichlet Pseudo-Relativistic Kinetic Energy Operator on a Bounded Domain. In: Annales Henri Poincare, Vol. 19, No. 12: pp. 3743-3781

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Continuing the series of works following Weyl's one-term asymptotic formula for the counting function of the eigenvalues of the Dirichlet Laplacian (Weyl in Math Ann 71(4):441-479, 1912) and the much later found two-term expansion on domains with highly regular boundary by Ivri (Funktsional Anal i Prilozhen 14(2):25-34, 1980) and Melrose (in: Proceedings of symposia in pure mathematics, vol XXXVI, pp 257-274, American Mathematical Society, 1980), we prove a two-term asymptotic expansion of the Nth Cesaro mean of the eigenvalues of with Dirichlet boundary condition on a bounded domain by Banuelos et al. (J Math Anal Appl 410(2):837-846, 2014) and Park and Song (Potential Anal 41(4):1273-1291, 2014).

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