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Analyse mathématique et calcul numérique pour les sciences et les techniques. Volume 5: Spectre des opérateurs. (Mathematical analysis and numerical methods for science and technology. Vol. 5: Spectrum of operators). Avec la collaboration de Michel Artola, Michel Cessenat, Jean-Michel Combes, Bruno Scheurer (Reproduction intégrale en 9 vol. brochés de l’ouvrage paru en trois tomes reliés, chez Masson en 1984 et 1985). Reproduction intégrale en 9 vol. brochés de l’ouvrage paru en trois tomes reliés, chez Masson en 1984 et 1985. (French) Zbl 0664.47003

Commissariat à l’Énergie Atomique, Gif-sur-Yvette (France). Inst. National des Sciences et Techniques Nucléaires. Collection Enseignement. Paris etc.: Masson. 574 p. FF 200.00 (1988).
This book comprises chapters 8, 9 and 10 of the work whose chapters 3 to 7 are reviewed above. Ch. 8 deals with spectral theory in Banach and Hilbert spaces with applications; the appendix contains a proof of the theorem of Krein-Rutman, which is a generalization of the Perron- Frobenius theorem to certain positive operators. Ch. 9 gives examples taken from electromagnetism and quantum mechanics. The short chapter 10 covers mixed problems and Tricomi’s equation in view of considering plane stationary compressible fluid flows.
Reviewer: R.Vaillancourt

MSC:

47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47A10 Spectrum, resolvent
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47F05 General theory of partial differential operators
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