Microlocal Analysis and Precise Spectral Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis and Precise Spectral Asymptotics write by Victor Ivrii. This book was released on 2013-03-14. Microlocal Analysis and Precise Spectral Asymptotics available in PDF, EPUB and Kindle. The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.
Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV
Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV write by Victor Ivrii. This book was released on 2019-09-11. Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV available in PDF, EPUB and Kindle. 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 methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.
Microlocal Analysis, Sharp Spectral Asymptotics and Applications III
Microlocal Analysis, Sharp Spectral Asymptotics and Applications III - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis, Sharp Spectral Asymptotics and Applications III write by Victor Ivrii. This book was released on 2019-09-12. Microlocal Analysis, Sharp Spectral Asymptotics and Applications III available in PDF, EPUB and Kindle. 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 methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis, Sharp Spectral Asymptotics and Applications V write by Victor Ivrii. This book was released on 2019-09-13. Microlocal Analysis, Sharp Spectral Asymptotics and Applications V available in PDF, EPUB and Kindle. 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 methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.
Microlocal Analysis, Sharp Spectral Asymptotics and Applications II
Microlocal Analysis, Sharp Spectral Asymptotics and Applications II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis, Sharp Spectral Asymptotics and Applications II write by Victor Ivrii. This book was released on 2019-09-11. Microlocal Analysis, Sharp Spectral Asymptotics and Applications II available in PDF, EPUB and Kindle. 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.
