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Author : Min-You Qi,L Rodino
Publisher : CRC Press
Page : 248 pages
File Size : 55,7 Mb
Release : 1996-05-20
Category : Mathematics
ISBN : 0582292123
Author : Min-You Qi,L Rodino
Publisher : Chapman and Hall/CRC
Page : 240 pages
File Size : 54,9 Mb
Release : 1996-05-20
Category : Mathematics
ISBN : 0582292123
Author : Luigi Rodino
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401156264
The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.
Author : Massimo Cicognani,Ferruccio Colombini,Daniele Del Santo
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 49,8 Mb
Release : 2013-03-12
Category : Mathematics
ISBN : 9781461463481
This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardy-type inequalities *linear and non-linear hyperbolic equations and systems *Schrödinger equations *water-wave equations *Euler-Poisson systems *Navier-Stokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource. Contributors T. Alazard P.I. Naumkin J.-M. Bony F. Nicola N. Burq T. Nishitani C. Cazacu T. Okaji J.-Y. Chemin M. Paicu E. Cordero A. Parmeggiani R. Danchin V. Petkov I. Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L. Rodino J. Huang M. Ruzhanky D. Lannes J.-C. Saut F. Linares N. Visciglia P.B. Mucha P. Zhang C. Mullaert E. Zuazua T. Narazaki C. Zuily
Author : Antonio Bove,Ferruccio Colombini,Daniele Del Santo
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 50,8 Mb
Release : 2007-12-28
Category : Mathematics
ISBN : 9780817645212
Covers phase space analysis methods, including microlocal analysis, and their applications to physics Treats the linear and nonnlinear aspects of the theory of PDEs Original articles are self-contained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace Excellent reference and resource for grad students and researchers in PDEs and related fields
Author : Goro Kato,Daniele C Struppa
Publisher : CRC Press
Page : 317 pages
File Size : 49,5 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9781000105186
"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Author : Alain Grigis
Publisher : Unknown
Page : 151 pages
File Size : 51,7 Mb
Release : 1994
Category : Differential operators
ISBN : 1139884921
This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.
Author : Victor Ivrii
Publisher : Springer Nature
Page : 739 pages
File Size : 52,6 Mb
Release : 2019-09-13
Category : Mathematics
ISBN : 9783030305611
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.
Author : Maria Mascarello,Luigi Rodino
Publisher : Wiley-VCH
Page : 360 pages
File Size : 54,6 Mb
Release : 1997-11-03
Category : Mathematics
ISBN : UOM:39015042989346
This book is devoted to the general theory of partial differential equations with multiple characteristics. The methods of the microlocal analysis are reviewed and used to prove recent results on local solvability, hypoellipticity, propagation of singularities in the frame of Sobolev spaces, Schwartz distributions, and Gevrey ultradistributions. The Cauchy problem is also considered.
Author : Yu.V. Egorov,M.A. Shubin
Publisher : Springer
Page : 244 pages
File Size : 43,8 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 3662092085
A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.
Author : Victor Ivrii
Publisher : Springer Nature
Page : 889 pages
File Size : 43,8 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305574
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.
Author : Victor Ivrii
Publisher : Springer Nature
Page : 525 pages
File Size : 55,5 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030305413
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.
Author : Victor Ivrii
Publisher : Springer Nature
Page : 729 pages
File Size : 44,6 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305376
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.
Author : Victor Ivrii
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 45,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662124963
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.
Author : Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Publisher : Springer Nature
Page : 533 pages
File Size : 50,8 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9783030361389
The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.