Ulteriori informazioni
The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.
Sommario
1. Test functions and distributions; 2. Differentiation and multiplication; 3. Distributions and compact support; 4. Tensor products; 5. Convolution; 6. Distribution kernels; 7. Co-ordinate transforms and pullbacks; 8. Fourier transforms; 9. Plancherel's theorem; 10. The Fourier-Laplace transform; Appendix. Topological vector spaces; 11. The calculus of wavefront sets.
Riassunto
In this classic graduate text, first published in 1999, the theory of distributions is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces; and also in this edition, the notion of the wavefront set of a distribution is introduced.
