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A spectral analogue of the Meinardus theorem on asymptotics of the number of partitions
Tatsuya Tate
Asymptotic Analysis 67 (2010) 101-123
arXiv: math/0702857v2 - DOI (math.FA)
Introduction has rewritten. In particular, the assumption in the main theorem has been changed. The assumption of main theorem in the old version is not suitable. Some mistakes are fixed. To appear in the journal Asymptotic Analysis
License: NONEXCLUSIVE-DISTRIB 1.0
Abstract: An asymptotic formula for the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold is given under a integrality assumption on the spectrum of the Hamiltonian. This is regarded as an analogue of the Meinardus theorem on asymptotics of the number of partitions of a positive integer.
Submitted to arXiv on 28 Feb. 2007