Автор: Bergeron, Nicolas Название: Spectrum of hyperbolic surfaces ISBN: 3319276646 ISBN-13(EAN): 9783319276649 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called "arithmetic hyperbolic surfaces", the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them.
After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.
The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Автор: Fabrizio Colombo; Irene Sabadini; Franciscus Somme Название: Analysis of Dirac Systems and Computational Algebra ISBN: 1461264693 ISBN-13(EAN): 9781461264699 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems
* All the necessary classical material is initially presented
* Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics
Описание: for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug- gesting the publication of these notes as a book.
Автор: Arno Bohm; Arno Bohm; J.D. Dollard; Manuel Gadella Название: Dirac Kets, Gamow Vectors and Gel`fand Triplets ISBN: 3662137518 ISBN-13(EAN): 9783662137512 Издательство: Springer Рейтинг: Цена: 11753.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Applications are given to physical theories of such phenomena as decaying states and resonances.
Автор: Levitan; I.S. Sargsjan Название: Sturm—Liouville and Dirac Operators ISBN: 0792309928 ISBN-13(EAN): 9780792309925 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 'Et moi, ...- si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point allC: .' human. race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'ttre of this series.
Автор: Waldyr A. Rodrigues; Edmundo C. Oliveira Название: The Many Faces of Maxwell, Dirac and Einstein Equations ISBN: 3642090389 ISBN-13(EAN): 9783642090387 Издательство: Springer Рейтинг: Цена: 16070.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories.
Автор: Waldyr A. Rodrigues, Jr; Edmundo Capelas de Olivei Название: The Many Faces of Maxwell, Dirac and Einstein Equations ISBN: 3319276360 ISBN-13(EAN): 9783319276366 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is an exposition of the algebra and calculus of differentialforms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to aformulation of important concepts of differential geometry indispensable for anin-depth understanding of space-time physics.The formalism discloses the hidden geometrical nature of spinor fields.
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