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Microlocal Analysis, Sharp Spectral Asymptotics and Applications I

Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics

  • Book
  • © 2019

Overview

Authors:
  1. Victor Ivrii

    1. Department of Mathematics, University of Toronto, Toronto, Canada

    View author publications

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  • 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 (8 chapters)

  1. Front Matter

    Pages I-XLIX
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  2. Semiclassical Microlocal Analysis

    1. Front Matter

      Pages 1-1
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    2. Introduction to Microlocal Analysis

      • Victor Ivrii
      Pages 2-125

    3. Propagation of Singularities in the Interior of the Domain

      • Victor Ivrii
      Pages 126-195

    4. Propagation of Singularities near the Boundary

      • Victor Ivrii
      Pages 196-284

  3. Local and Microlocal Semiclassical Spectral Asymptotics in the Interior of the Domain

    1. Front Matter

      Pages 285-285
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    2. General Theory in the Interior of the Domain

      • Victor Ivrii
      Pages 286-406

    3. Scalar Operators in the Interior of the Domain. Rescaling Technique

      • Victor Ivrii
      Pages 407-520

    4. Operators in the Interior of Domain. Esoteric Theory

      • Victor Ivrii
      Pages 521-621

  4. Local and Microlocal Semiclassical Spectral Asymptotics Near the Boundary

    1. Front Matter

      Pages 622-622
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    2. Standard Local Semiclassical Spectral Asymptotics near the Boundary

      • Victor Ivrii
      Pages 623-741

    3. Standard Local Semiclassical Spectral Asymptotics near the Boundary. Miscellaneous

      • Victor Ivrii
      Pages 742-800

  5. Back Matter

    Pages 801-889
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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 general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.




Authors and Affiliations

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Victor Ivrii

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 I

  • Book Subtitle: Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics

  • Authors: Victor Ivrii

  • DOI: https://doi.org/10.1007/978-3-030-30557-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-30556-7Published: 26 September 2019

  • Softcover ISBN: 978-3-030-30559-8Published: 26 September 2020

  • eBook ISBN: 978-3-030-30557-4Published: 12 September 2019

  • Edition Number: 1

  • Number of Pages: XLIX, 889

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis, Mathematical Physics

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