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FUNCTIONAL ANALYSIS 2

CODE 61705
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    This course deals with impotant topics in Functional Analysis and Operator Theory, which complete and develop the contents of the course "Analisi Funzionale 1".

    The lectures are delivered in Italian.

    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

    This course provides some fundamental contents in Functional Analysis and Operator Theory. Students are expected to understand the concepts and the proofs that have been shown in the classes. In particular, they are expected to be able to provide proofs consisting in simple variants of the proofs that have been shown in the classes, to construct examples and to solve exercises about the topics developed in the course.

    PREREQUISITES

    Prerequisites: the contents of the course "AF 1".

    TEACHING METHODS

    Teaching style: lectures (52 hours), given in the mode that will be decided by the University of Genova. Some of the lectures will be devoted to exercises.

    SYLLABUS/CONTENT

    Quotient normed spaces; reflexivity; 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

    W. Rudin: Real and Complex Analysis

    W. Rudin: Functional Analysis

    TEACHERS AND EXAM BOARD

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    EXAMS

    EXAM DESCRIPTION

    Written and oral tests. The written test lasts two hours and consists of two exercises concerning the contents of the syllabus. During the written test, students are allowed to consult the notes they have taken in the classes, as well as textbooks. The oral test can be taken whichever grade the student has got in the written test, and must be taken in the same round of the written test.

    ASSESSMENT METHODS

    There will be both a written test and an oral one. Each of them is intended to verify understanding by the student of the concepts and of the proofs developed in the classes, as well as ability in producing proofs consisting of simple variants of the proofs that have been shown in the classes, in constructing examples and in solving exercises concerning the syllabus.

    FURTHER INFORMATION

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