|Teoria||9||I semestre||Sisto Baldo, Giandomenico Orlandi|
|Esercitazioni||3||I semestre||Sisto Baldo|
|Teoria||Monday||4:30 PM - 6:30 PM||lesson||Lecture Hall M|
|Teoria||Tuesday||3:30 PM - 6:30 PM||lesson||Lecture Hall M|
|Teoria||Wednesday||4:30 PM - 6:30 PM||lesson||Lecture Hall M|
|Teoria||Thursday||4:30 PM - 6:30 PM||lesson||Lecture Hall M|
The course introduces to the basic concepts of measure theory (Lebesgue and abstract) and of modern functional analysis, with particular emphasis on Banach and Hilbert spaces. Whenever possible, abstract results will be presented together with applications to concrete function spaces and problems: the aim is to show how these techniques are useful in the different fields of pure and applied mathematics.
Lebesgue measure and integral. Outer measures, abstract integration, integral convergence theorems. Banach spaces and their duals. Theorems of Hahn-Banach, of the closed graph, of the open mapping, of Banach-Steinhaus. Reflexive spaces. Spaces of sequences. Lp and W1,p spaces: functional properties and density/compactness results. Hilbert spaces, Hilbert bases, abstract Fourier series. Weak convergence and weak compactness. Spectral theory for self adjoint, compact operators. Basic notions from the theory of distributions.
Written and oral exam.
|Title||Format (Language, Size, Publication date)|
|Diario delle lezioni del prof. Orlandi||pdf (it, 103 KB, 25/01/11)|