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Microlocal Analysis, Sharp Spectral Asymptotics and Applications I: Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics

✍ Scribed by Victor Ivrii

Publisher
Springer International Publishing
Year
2019
Tongue
English
Leaves
938
Edition
1st ed. 2019
Category
Library
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✦ Synopsis

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 β€œsmall” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic SchrΓΆdinger operator, miscellaneous problems, and multiparticle quantum theory.

In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.




✦ Table of Contents

Front Matter ....Pages I-XLIX
Front Matter ....Pages 1-1
Introduction to Microlocal Analysis (Victor Ivrii)....Pages 2-125
Propagation of Singularities in the Interior of the Domain (Victor Ivrii)....Pages 126-195
Propagation of Singularities near the Boundary (Victor Ivrii)....Pages 196-284
Front Matter ....Pages 285-285
General Theory in the Interior of the Domain (Victor Ivrii)....Pages 286-406
Scalar Operators in the Interior of the Domain. Rescaling Technique (Victor Ivrii)....Pages 407-520
Operators in the Interior of Domain. Esoteric Theory (Victor Ivrii)....Pages 521-621
Front Matter ....Pages 622-622
Standard Local Semiclassical Spectral Asymptotics near the Boundary (Victor Ivrii)....Pages 623-741
Standard Local Semiclassical Spectral Asymptotics near the Boundary. Miscellaneous (Victor Ivrii)....Pages 742-800
Back Matter ....Pages 801-889

✦ Subjects

Mathematics; Analysis; Mathematical Physics

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