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Microlocal Analysis, Sharp Spectral Asymptotics and Applications II

Functional Methods and Eigenvalue Asymptotics

  • Victor Ivrii
Book

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Estimates of the Spectrum

    1. Front Matter
      Pages 1-1
    2. Victor Ivrii
      Pages 2-44
  3. Asymptotics of Spectra

    1. Front Matter
      Pages 94-94
    2. Victor Ivrii
      Pages 95-261
    3. Victor Ivrii
      Pages 262-439
  4. Back Matter
    Pages 440-525

About this book

Introduction

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.

Keywords

Microlocal Analysis Propagation of Singularities Sharp Spectral Asymptotics Schrodinger Operator Ground State Energy

Authors and affiliations

  • Victor Ivrii
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

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