Описание: Non-smooth theory and higher dimensions.- Irregular coefficients in dimensions 2, 3.- Full-rank case.- Non-full-rank case.- 4D-Schrцdinger with degenerating magnetic field.- 4D-Schrцdinger Operator with the strong magnetic field.- Eigenvalue asymptotics for Schrцdinger and dirac operators with the strong magnetic field.- Eigenvalue asymptotics: 2D case.- Eigenvalue asymptotics: 3D case.
Описание: 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 Schr?dinger 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.
Описание: Smooth theory in dimensions 2 and 3.- Standard Theory.- 2D degenerating magnetic Schrцdinger operator.- 2D magnetic Schrцdinger near boundary.- Magnetic Schrцdinger operator: short loops.- Dirac operator with strong magnetic field.
Описание: No magnetic field case.- The case of external magnetic field.- The case of self-generated magnetic field, - The case of combined magnetic field.- Articles on asymptotics.- 100 years of Weyl's law
Описание: 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 Schr?dinger 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.
Описание: 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 Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I, II and III are applied to the Schr?dinger and Dirac operators in non-smooth settings and in higher dimensions.
Описание: 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 Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I and II are applied to the Schr?dinger and Dirac operators in smooth settings in dimensions 2 and 3.
Описание: 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 Schr?dinger 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.
Автор: Victor Ivrii Название: Microlocal Analysis and Precise Spectral Asymptotics ISBN: 3642083072 ISBN-13(EAN): 9783642083075 Издательство: Springer Рейтинг: Цена: 20263.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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; to provide furt her progress and only a couple of not very exciting problems remained to be solved.
Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Название: Asymptotics, Nonparametrics, and Time Series ISBN: 036739992X ISBN-13(EAN): 9780367399924 Издательство: Taylor&Francis Рейтинг: Цена: 9798.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."
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