Overview
- Research monograph for researchers and graduate students in Mathematics and Mathematical Physics
- Most comprehensive work about the topic
- Use of technique, developed by the author during more than 40 years
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Table of contents (4 chapters)
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Front Matter
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Estimates of the Spectrum
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Front Matter
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Asymptotics of Spectra
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
VICTOR IVRII is a professor of mathematics at the University of Toronto. His areas of specialization are analysis, microlocal analysis, spectral theory, partial differential equations and applications to mathematical physics. He proved the Weyl conjecture in 1979, and together with Israel M. Sigal he justified the Scott correction term for heavy atoms and molecules in 1992. He is a Fellow of the Royal Society of Canada (since 1998) and of American Mathematical Society (since 2012).
Bibliographic Information
Book Title: Microlocal Analysis, Sharp Spectral Asymptotics and Applications II
Book Subtitle: Functional Methods and Eigenvalue Asymptotics
Authors: Victor Ivrii
DOI: https://doi.org/10.1007/978-3-030-30541-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-30540-6Published: 23 September 2019
Softcover ISBN: 978-3-030-30543-7Published: 23 September 2020
eBook ISBN: 978-3-030-30541-3Published: 11 September 2019
Edition Number: 1
Number of Pages: XIX, 525
Number of Illustrations: 1 b/w illustrations
Topics: Analysis, Mathematical Physics