OVERVIEW

Language: Italian

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.

Exam Board

ANDREA BRUNO CARBONARO (President)

ADA ARUFFO

GIOVANNI ALBERTI (President Substitute)

Teaching methods

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

ADVANCED ANALYSIS 1

Exam description

Oral.