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Microlocal Analysis, Sharp Spectral Asymptotics and Applications II: Functional Methods and Eigenvalue Asymptotics
Paperback
CalculusGeneral MathematicsPhysics
ISBN13: 9783030305437
Publisher: Springer Nature
Published: Sep 23 2020
Pages: 525
Weight: 1.67
Height: 1.11 Width: 6.14 Depth: 9.21
Language: English
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.
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