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PDF книги » Математика » Kalnins E.G. - Separation of Variables for Riemannian Spaces of Constant Curvature

Kalnins E.G. - Separation of Variables for Riemannian Spaces of Constant Curvature

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Название: Separation of Variables for Riemannian Spaces of Constant Curvature
Автор: Kalnins E.G.
Категория: Математика
Тип: Книга
Дата: 04.01.2009 12:10:56
Скачано: 27
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Описание: This book arose from the desire to give a compact and, in a somewhat restricted sense, complete treatment of the subject of separation of variables. The only book already available on the specific topic of separation of variables is that of Miller. This earlier work gives an excellent treatment of the relationships between the classical special functions of mathematical physics and Lie group theory. The aim of the present work is to show how all the actual inequivalent separable coordinate systems can be computed for the Hamilton-Jacobi and Helmholtz equations on real positive definite Riemannian spaces of constant curvature. The results necessary for the solution of this problem are developed in the text. This allows the reader to obtain a feel for the subject without the necessity to read widely in the literature. It is in this spirit that the book has been written. Proofs that are central to the computation of all the inequivalent coordinate systems mentioned above are given in full; the more general results of the theory are often quoted, suitable references being given. We also, on occasion, appeal to the reader's intuition. In Chapter 1 we give some introductory comments on the subject of separation of variables. Included here are the basic notions of additive and multiplicative separation of variables as well as an intuitive discussion of the basic problems of the associated theory of separation of variables. Chapter 2 sketches the historical development of the theory of separation of variables, providing a useful summary and extracting, from the many contributions, the most significant results. It also provides an indication of the degrees of freedom available in the specification of a separable
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