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
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The 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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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following3 modules among the followingLegend | 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 analysis (2019/2020)
Teaching code
4S001101
Academic staff
Coordinator
Credits
12
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Period
I semestre dal Oct 1, 2019 al Jan 31, 2020.
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. At the end of the course, students must be able to read and understand advanced texts on functional analysis. They must be able to solve problems in the discipline.
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.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| Brezis, Haïm | Analisi funzionale. Teoria e applicazioni | Liguori | 1986 | 8820715015 | |
| A.N. Kolmogorov, S.V. Fomin | Elementi di teoria delle funzioni e di analisi funzionale (Edizione 4) | MIR | 1980 | xxxx | |
| Kolmogorov, A.; Fomin, S. | Elements of the Theory of Functions and Functional Analysis | Dover Publications | 1999 | 0486406830 | |
| Haim Brezis | Functional Analysis, Sobolev Spaces and Partial Differential Equations | Springer | 2011 | 0387709134 |
Examination Methods
Written and oral test.
The written test will be based on the solution of open-form problems. The oral test will require a discussion of the written test and answering some questions proposed in open form.
The aim is to evaluate the skills of the students in proving statements and in solving problems, by employing some of the mathematical machinery and of the techniques studied in the course.
The final grade in a scale from 0 to 30 (best), with a pass mark of 18, is given by the arithmetic average of the marks of the written and of the oral part.
