| Center |
| Faculty of Mathematics |
| Departament |
| Mathematical Analysis |
| Lecturers in charge |
| F8110 - PABLO GALINDO PASTOR |
| Met. Docent |
| There are two parts, one theoretical and another of practical character. The teacher will develop the theoretical part. In the practical part the students will discuss and solve a number of exercises related to the theory; such exercises will be provided by the teacher |
| Met. Avaluació |
| An examination will be held in each convocatory. It will consist of a theoretical part and a practical one. |
| Bibliografia |
| - Azid el Kacimi, Introduccion al Analisis Funcional. Ed. Reverte, 1993 -J. B. Conway, A Course of Functional Analysis. Second Edition. Ed. Springer, 1990. -G.J.O. Jameson, Topology and Normed Spaces. Ed. Chapman and Hall, 1982. -L.Lusternik & V. Sobolev, Precis d'Analyse Fonctionelle. Ed. Mir, 1989. -A.E. Taylor & D. C. Lay, Introduction to Functional Analysis. Ed. Wiley and Sons, 1980. |
| Continguts |
| 1. Normed spaces: Norms on a vector space. Examples of normed and Banach spaces. Some sequence and function Banach spaces. 2. Linear mappings: Norm of a linear mapping between normed spaces. The space of linear and continuous mappings. Examples, the case of the integral operators. Estimating the norm of some operators. 3. Hilbert spaces: Definition. Examples. Ortogonal and ortonormal systems.Paralelogram's rule. The projection along a closed subspace. 4. Spectral analysis of operators and compact operators: The spectrum of an operator. Eigenvalues and eigenvectors. Compact operators. The spectral descomposition theorem. Some applications. |
| Objetius |
| Let the student know the Functional Analysis foundations so that he/she learns the basic methods and tools of the Banach and Hilbert space theories as well as those of the operator theory. |
| URL de Fitxa |