| Center |
| Faculty of Mathematics |
| Departament |
| Mathematical Analysis |
| Lecturers in charge |
| F6092 - JOSE M MAZON RUIZ |
| Met. Docent |
| The classes will consist of two sessions with theoretical content (about 2 hours and a half) and one of practical content(about 1 hour and a half). Some sheets of problems and questions will be provided during the course. |
| Met. Avaluació |
| There will be an exam with some theoretical and practical. The problems solved by the students during the class will be taken into account. |
| Bibliografia |
| Apostol, T.M., Análisis Matemático. Reverté, 1976. Duoandikoetxea, J., Análisis de Fourier. Addison-Wesley, 1995. Dym, H., McKean, H.P. Fourier Series and Integrals. Academic Press, 1972. Katznelson, Y. Introduction to Harmonic Analysis. Dover Publ., 1976. |
| Continguts |
| The content of the subject is mainly devoted to the study of the notion of convolution (for the torus and for Rn) and some of the applications of it to approximation and regularization of functions, and the notion of Fourier series, with different summability methods associated to it, according to the summability kernel considered in each case. The main results shown during the course concern different types of convergence of the Fourier series and Plancherel's theorem. |
| Objetius |
| The aim is that the students get used to the main basic tools and techniques in Fourier Analysis on the torus and on the real line. By the end of the course they should be able compute Fourier series and Fourier transforms of some elementary functions and to use them for applications. |
| URL de Fitxa |