- Docente: Angelo Cavallucci
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 0436)
Learning outcomes
Introduction to: Fourier Transform, Hilbert and Banach Spaces, weak derivatives
Course contents
Lp Spaces: Completeness. Density of some function classes. Regularisation. Fourier Transform in L^1, L^2. Spaces H^s and their traces. Hilbert Spaces: Orthogonal projection. Dual space. Orthonormal basis. Fourier Series. Weak convergence .Minimum of convex functions. Banach Spaces : continuous or compact linear mappings; elements of differential calculus and implicit function theorem.
Readings/Bibliography
* B. Pini, Terzo corso di analisi matematica, CLUEB, Bologna, 1977-79 * B. Pini, Lezioni di analisi matematica di secondo livello, Parte prima, CLUEB, Bologna * W. Rudin, Analisi reale e complessa, Boringhieri, Torino, 1974 * W. Rudin, Functional analysis, Mc Grow-Hill, New York, 1973
Teaching methods
Front lessons.
Assessment methods
Written and oral examination
Office hours
See the website of Angelo Cavallucci