Sturm—Liouville and Dirac Operators, Levitan; I.S. Sargsjan

Автор: Bernhelm Boo?-Bavnbek; Krzysztof P. Wojciechhowski
Название: Elliptic Boundary Problems for Dirac Operators
ISBN: 1461267137 ISBN-13(EAN): 9781461267133
Издательство: Springer
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Автор: Fabrizio Colombo; Irene Sabadini; Franciscus Somme
Название: Analysis of Dirac Systems and Computational Algebra
ISBN: 0817642552 ISBN-13(EAN): 9780817642556
Издательство: Springer
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Описание: Examines systems of linear PDEs with constant coefficients, focusing attention on null solutions of Dirac systems. This provides a different way to look at some important questions which arise when one tries to develop multi-dimensional theories.

Автор: Levitan; I.S. Sargsjan
Название: Sturm—Liouville and Dirac Operators
ISBN: 0792309928 ISBN-13(EAN): 9780792309925
Издательство: Springer
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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: Vladimir Kozlov; Vladimir Maz`ya
Название: Theory of a Higher-Order Sturm-Liouville Equation
ISBN: 3540630651 ISBN-13(EAN): 9783540630654
Издательство: Springer
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Описание: The aim of this book is to develop a detailed theory of a generalized Sturm-Liouville equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions, and Green`s functions, asymptotic properties of solutions at infinity.

Автор: Jan Cnops
Название: An Introduction to Dirac Operators on Manifolds
ISBN: 1461265967 ISBN-13(EAN): 9781461265962
Издательство: Springer
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Описание: Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory.

Автор: Bernhelm Boo?-Bavnbek; Krzysztof P. Wojciechhowski
Название: Elliptic Boundary Problems for Dirac Operators
ISBN: 0817636811 ISBN-13(EAN): 9780817636814
Издательство: Springer
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Описание: Elliptic boundary problems have enjoyed interest recently, espe- cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec- ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con- texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif- ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.

Автор: Heinz Otto Cordes
Название: Precisely Predictable Dirac Observables
ISBN: 9048172993 ISBN-13(EAN): 9789048172993
Издательство: Springer
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Описание: This work presents a Clean Quantum Theory of the Electron, based on Dirac`s equation. "Clean" in the sense of a complete mathematical explanation of the well known paradoxes of Dirac`s theory and a connection to classical theory.