On an algorithm for two-term spectral asymptotic formulas
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909099881398272 |
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| author | Liu, Genqian |
| author_facet | Liu, Genqian |
| contents | In the book [Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators, Amer. Math. Soc., Providence, RI, 1997], a key and central ``algorithm'' was established, by which the coefficients of two-term asymptotic expansions of the eigenvalue counting functions can be explicitly calculated for many partial differential operators under an additional geometric assumption. In this paper, we give a counter-example to this ``algorithm'' by discussing the case of elastic eigenvalues. This implies that the most conclusions in the above book written by Yu. Safarov and D. Vassiliev are fundamentally wrong because they are based on the erroneous ``algorithm''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07475 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On an algorithm for two-term spectral asymptotic formulas Liu, Genqian Differential Geometry Analysis of PDEs 53C21 (Primary), 58J50 (Secondary) In the book [Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators, Amer. Math. Soc., Providence, RI, 1997], a key and central ``algorithm'' was established, by which the coefficients of two-term asymptotic expansions of the eigenvalue counting functions can be explicitly calculated for many partial differential operators under an additional geometric assumption. In this paper, we give a counter-example to this ``algorithm'' by discussing the case of elastic eigenvalues. This implies that the most conclusions in the above book written by Yu. Safarov and D. Vassiliev are fundamentally wrong because they are based on the erroneous ``algorithm''. |
| title | On an algorithm for two-term spectral asymptotic formulas |
| topic | Differential Geometry Analysis of PDEs 53C21 (Primary), 58J50 (Secondary) |
| url | https://arxiv.org/abs/2309.07475 |