OVERVIEW

The lectures are delivered in Italian.

This course deals with important topics in Functional Analysis and Operator Theory, which complete and develop the ones already covered in the previous course of Functional Analysis 1.

AIMS AND CONTENT

LEARNING OUTCOMES

To provide some fundamental contents in Functional Analysis and Operator Theory that are considered important for the students who want to follow a PhD, or anyway aim to get a well grounded knowledge in the basic branches of Mathematics.

AIMS AND LEARNING OUTCOMES

To provide some fundamental contents in Functional Analysis and Operator Theory.

Expected learning outcomes:

The students will become acquainted with the concepts and proofs carried out in class and how they are used in practice to solve exercises; moreover they will know how to produce easy variants of demonstrations seen and construct examples on topics covered in this course.

PREREQUISITES

Mathematical Analysis I, 2, 3 and 4, Linear Algebra and Analitic Geometry, Geometry 1, Functional Analysis 1.

TEACHING METHODS

Lectures (52 hours). Both theory and exercises are presented by the teacher in the usual way. Moreover some tutorial exercitations will be carried out during the semester.

SYLLABUS/CONTENT

Weak topologies; compactness in spaces of continuous functions: the Ascoli-Arzelà theorem; elements of operator theory: the spectrum, the adjoint operator, compact operators, the spectral theorem for compact selfadjoint operators, the spectral radius.

RECOMMENDED READING/BIBLIOGRAPHY

A.E. Taylor, D.C. Lay: Introduction to Functional Analysis, 2nd edition

N. Dunford, J.T. Schwartz - Linear Operators. Part I: General Theory - Interscience 1957

W. Rudin - Real and Complex Analysis - McGraw-Hill 1970

W. Rudin: Functional Analysis

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The start date of classes will be decided by the Degree Course Board in Mathematics.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written and oral tests. Oral test, which students can access whatever the outcome of written test, has to be taken in the same exam session of written test.

Students with disabilities or specific learning disorders (SLD) are reminded that, in order to be enabled to request specfic arrangements during exams, they must before insert certification on the website of the University, on the page servizionline.unige.it section “Studenti”. All relevant information is available on the University website: https://unige.it/disabilita-dsa

ASSESSMENT METHODS

The written examination consists in an exercise about the topics covered in this course. In this test the ability to apply theoretical results in concrete situations is evaluated.

The test lasts an hour and a half and it is possible to consult the notes and textbooks.

In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding, the knowledge of the concepts, and the skills in using them, acquired by the students.

FURTHER INFORMATION

Attendance is recommended.

Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teacher about the course.

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)
• Additional time (+50% disability/invalidity)
• Additional time during oral exams to organise the answer
• Calculator (programmable and graphing calculators are not allowed)
• Conceptual Maps
• Tables and/or Forms
• Take the exam in written form
• Take the exam in oral form
• Tutor reader (for written tests only)
• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it