Linear operators in spaces with an indefinite metric : T.Ya. Azizov and I.S. Iokhvidov (translated by E.R. Dawson), Wiley, Chichester, 1989. 304 pp., £39.95, ISBN 0-471-92129-7
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 87 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0378-4754
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✦ Synopsis
in this book, on the basis of the geometry of spaces with an indefinite metric (chiefly the bein and Pontryagin spaces), the authors develop the foundations of the theory of linear operators in these spaces. After an introductory chapter on geometry, :aken at a fairly leisurely pace for the benefit of the novice, the book goes on to give a full account of the theory of operators, including the theory of invariant subspaces, spectral questions, and the question of the extension of operators. Some applications are also described.
Problems for the reader are provided at the end of each section, with hints or further references. There is also an extensive bibliography.
The subject of linear operators in spaces with an indefinite metric has wide-ranging and varied applications. It will be of interest to graduate students and researchers working in the areas of differential equations, moment problems, damped oscillations of mechanical systems, representation theory of groups, geometry and theoretical physics, as well as to those interested in the theory for its own sake. Contents 1. The geometry of spaces with an indefinite metric 2. Fundamental classes of operators in spaces with an indefinite metric 3. Invariant semi-definite subspaces 4. Spectral topics and some applications 5. Theory of extensions of isometric and symmetric operators in spaces with an indefinite metric References Index.