Mathematical analysis and numerical methods for science and technology. (In six volumes). Volume 2: Functional and variational methods. With the collaboration of Michel Artola, Marc Authier, Philippe Bénilan, Michel Cessenat, Jean-Michel Combes, Hélène Lanchon, Bertrand Mercier, Claue Wild, Claude Zuily. Transl. from the French by Ian N. Sneddon. (English) Zbl 0664.47001
Berlin etc.: Springer-Verlag. xv, 561 p. DM 198.00 (1988).
This book comprises chapters 3 to 7 of a 21-chapter advanced text for scientists and engineers which studies linear distributed models, i.e. partial differential equations, for important problems in physics by means of general methods of linear functional analysis. Ch. 3 covers Fourier series, Mellin and Hankel transforms, discrete and fast Fourier transforms. Ch. 4 deals with Sobolev spaces. Ch. 5 treats linear differential operators. Ch. 6 reviews the theory of linear operators in Banach and Hilbert spaces. Ch. 7, which deals with linear variational problems and regularity of their solutions, ends with an appendix on theory of distributions. The style of presentation enjoys the clarity which characterizes the Lions’ school.
Reviewer: R.Vaillancourt
MSC:
| 47-02 | Research exposition (monographs, survey articles) pertaining to operator theory |
| 47F05 | General theory of partial differential operators |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46F10 | Operations with distributions and generalized functions |
| 35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |
| 46F12 | Integral transforms in distribution spaces |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35A15 | Variational methods applied to PDEs |
| 47A10 | Spectrum, resolvent |
