Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
Modules | Credits | TAF | SSD |
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2° Year activated in the A.Y. 2012/2013
Modules | Credits | TAF | SSD |
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Un insegnamento a scelta (insegnamenti seminariali ad esclusione di Psicologia dell'educazione e Matematica finanziaria)
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Un insegnamento a scelta (insegnamenti seminariali ad esclusione di Psicologia dell'educazione e Matematica finanziaria)
Modules | Credits | TAF | SSD |
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Functional anaysis (2011/2012)
Teaching code
4S02813
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
The teaching is organized as follows:
Teoria
Esercitazioni
Credits
3
Period
I semestre
Academic staff
Marco Squassina
Learning outcomes
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.
Program
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.
Examination Methods
Written and oral exam.
Teaching materials e documents
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Diario delle lezioni del prof. Orlandi (it, 135 KB, 1/25/12)
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Risultati Esercitazione Scritta del 20/12/2011 (it, 30 KB, 12/22/11)
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Esercizi di Analisi Funzionale: Foglio 1 (it, 18 KB, 11/3/11)
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Esercizi di Analisi Funzionale: Foglio 2 (it, 17 KB, 11/15/11)
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Esercizi di Analisi Funzionale: Foglio 3 (it, 19 KB, 12/15/11)
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Esercizi di Analisi Funzionale: Foglio 4 (it, 27 KB, 12/15/11)
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Esercizi di Analisi Funzionale: Foglio 5 (it, 23 KB, 1/31/12)