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Microlocal Analysis, Sharp Spectral Asymptotics and Applications II : Functional Methods and Eigenvalue Asymptotics. 2019 ed..
・ISBN 978-3-030-30540-6 hard EUR 119.99
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| 著者・編者 | Ivrii, Victor, |
|---|---|
| 出版社 | (Springer Nature Switzerland AG, SZ) |
| 出版年月 | 2019 |
| ページ数 | 525 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-14811＞ |
解説
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in "small" domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schroedinger operator, miscellaneous problems, and multiparticle quantum theory.
In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.