| Center |
| Faculty of Mathematics |
| Departament |
| Mathematical Analysis |
| Lecturers in charge |
| G7191 - MARIA CARMEN FERNANDEZ ROSELL |
| Met. Docent |
| Theorical lectures and exercises. |
| Met. Avaluació |
| Final examination and project work |
| Bibliografia |
| Al-Gwaiz, M.A Theory of Distributions.. Marcel Dekker, 1992. Barros Neto, J. An Introduction to the Theory of Distributions. Marcel Dekker,1973. Dautray, R., Lions, J. L. Analyse Mathématique et Calcul Numérique pour les Sciences et les Tecniques. Masson, 1984. Folland, G. B. Introduction to Partial Differential Equations. Princeton Univ. Press, 1976. Hörmander, L. Linear Partial Differential Equations. Springer-Verlag, 1969. Kesavan, S. Topics in Functional Analysis. , John Wiley and Sons, 1989. Rudin, W. Functional Analysis. McGrw-Hill, 1973. Schwartz, L. Théorie des Distributions. Hermann, 1973. Stricchartz, R. A Guide to Distributions Theory and Fourier Tr |
| Continguts |
| The space D(W). Multiíndexes, the space of test functions, regularized sequences, partitions of unity. The space D'(W) of distributions. Calculus with distributions. Support of a function. Support of a distribution, distributions with compact support. Convolution of distributions. The Fourier transform. Fourier transform of a function of L1(RN). Fourier transform of a function of L2(RN), tempered distributions, examples, Fourier transforms of tempered distributions. Fourier transform of distributions with compact support. Fundamental solutions. The Malgrange-Ehrenpreis theorem. Examples. |
| Objetius |
| This course pretends to introduce the student into L. Schwartz's theory of distributions, as well as to give some of its applications to partial differential equations. |
| URL de Fitxa |