Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV: Magnetic Schrцdinger Operator 2, Ivrii Victor
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications II ISBN: 3030305406 ISBN-13(EAN): 9783030305406 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V ISBN: 3030305600 ISBN-13(EAN): 9783030305604 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV ISBN: 3030305449 ISBN-13(EAN): 9783030305444 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications III ISBN: 3030305368 ISBN-13(EAN): 9783030305369 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications I ISBN: 3030305562 ISBN-13(EAN): 9783030305567 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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: Ivrii Victor Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V: Applications to Quantum Theory and Miscellaneous Problems ISBN: 3030305635 ISBN-13(EAN): 9783030305635 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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
Автор: Victor Ivrii Название: Microlocal Analysis and Precise Spectral Asymptotics ISBN: 3642083072 ISBN-13(EAN): 9783642083075 Издательство: Springer Рейтинг: Цена: 135090.00 T 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.
Автор: J.M. Bony; Lamberto Cattabriga; G. Grubb; Luigi Ro Название: Microlocal Analysis and Applications ISBN: 354054948X ISBN-13(EAN): 9783540549482 Издательство: Springer Рейтинг: Цена: 32560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This volume is comprised of a series of lectures given during a mathematical conference on partial differential equations and Schroedinger equations.
Автор: Luigi Rodino Название: Microlocal Analysis and Spectral Theory ISBN: 9401063710 ISBN-13(EAN): 9789401063715 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of the NATO Advanced Study Institute, Il Ciocco, Castelvecchio Pascoli (Lucca), Italy, 23 September-3 October 1996
Автор: Veliev Oktay Название: Multidimensional Periodic Schrцdinger Operator: Perturbation Theory and Applications ISBN: 3030245772 ISBN-13(EAN): 9783030245771 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Поставка под заказ. Описание: This book describes the direct and inverse problems of the multidimensional Schr?dinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe–Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow.
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