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Microlocal analysis, sharp spectral asymptotics and applications. II, Functional methods and Eigenvalue asymptotics / Victor Ivrii.

9783030305413 (electronic book)
3030305414 (electronic book)
9783030305406

https://doi.org/10.1007/978-3-030-30541-3
https://doi.org/10.1007/978-3-030-30

Cham : Springer, [2019]

©2019

English

1 online resource

10.1007/978-3-030-30541-3 doi
10.1007/978-3-030-30

QA299.6 .I87 2019eb

515/.7242

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 Schrödinger 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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed September 23, 2019).

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