Microlocal Analysis, Sharp Spectral Asymptotics and Applications II: Functional Methods and Eigenvalue Asymptotics

✍ Scribed by Victor Ivrii

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 544
• Edition: 1st ed. 2019
• Category: Library

✦ 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 “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.

✦ Table of Contents

Front Matter ....Pages I-XIX
Front Matter ....Pages 1-1
Estimates of the Negative Spectrum (Victor Ivrii)....Pages 2-44
Estimates of the Spectrum in the Interval (Victor Ivrii)....Pages 45-93
Front Matter ....Pages 94-94
Weyl Asymptotics of Spectra (Victor Ivrii)....Pages 95-261
Miscellaneous Asymptotics of Spectra (Victor Ivrii)....Pages 262-439
Back Matter ....Pages 440-525

✦ Subjects

Mathematics; Analysis; Mathematical Physics