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ADVANCED ANALYSIS 1

CODE 61683
ACADEMIC YEAR 2021/2022
CREDITS
  • 8 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • 8 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    Language: Italian

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The course aims to provide an introduction to distribution theory and some of its applications

    TEACHING METHODS

    Teaching style: In presence

    SYLLABUS/CONTENT

    Convolution of two functions.

    Locally convex topological vector spaces.

    Definition of a distribution. The space of test functions and the space of distributions. Order of a distribution. Distributions of order 0. Calculus on distributions. Compactly supported distributions. Distributions supported in a point. Regularization of divergent integrals. Convolution of a distribution with a test function. Convolution of two distributions. Analytic continuation of distributions.

    Fundamental solutions of constant coefficients operators. Hypoelliptic operators. Parametrics. The local structure of distributions.

    Fourier transform. Temperated distributions. Fundamental solutions of Laplace and heat operators. The Cauchy problem for the heat operator. Fourier transform of compactly supported distributions. Paley-Wiener theorems. Sobolev spaces (definition). The Cauchy problem for the wave operator. Finite speed of propagation. Fundamental solution of the wave operator.

    The Schwartz kernel theorem.

    TEACHERS AND EXAM BOARD

    Exam Board

    ANDREA BRUNO CARBONARO (President)

    ADA ARUFFO

    GIOVANNI ALBERTI (President Substitute)

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    Class schedule

    ADVANCED ANALYSIS 1

    EXAMS

    EXAM DESCRIPTION

    Oral.