Functional anaysis (2011/2012)

Course code 4S02813   Credits 12   Coordinator Sisto Baldo Study courses to which this belongs Master's Degree in Mathematics   Disciplinary sector MAT/05 - Mathematical analysis Teaching language Italian

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Teaching is organised as follows:

Lecture timetable

Educational objectives

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.

Syllabus

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.

Exam methods

Written and oral exam.

Teaching aids
Activity	Title	Format (Language, Size, Publication date)
Teoria	Diario delle lezioni del prof. Orlandi	pdf (it, 135.892 KB, 1/25/12)
Teoria	Risultati Esercitazione Scritta del 20/12/2011	pdf (it, 30.224 KB, 12/22/11)
Esercitazioni	Esercizi di Analisi Funzionale: Foglio 1	pdf (it, 18.804 KB, 11/3/11)
Esercitazioni	Esercizi di Analisi Funzionale: Foglio 2	pdf (it, 17.994 KB, 11/15/11)
Esercitazioni	Esercizi di Analisi Funzionale: Foglio 3	pdf (it, 19.601 KB, 12/15/11)
Esercitazioni	Esercizi di Analisi Funzionale: Foglio 4	pdf (it, 27.471 KB, 12/15/11)
Esercitazioni	Esercizi di Analisi Funzionale: Foglio 5	pdf (it, 23.188 KB, 1/31/12)

Statistics on students' past performance (Art. 2 del D.M. 31/10/2007, n. 544)

Data from AA 2011/2012 based on 9 students. I valori in percentuale sono arrotondati al numero intero più vicino.