CODE  61683 

ACADEMIC YEAR  2021/2022 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  2° Semester 
TEACHING MATERIALS  AULAWEB 
Language: Italian
The course aims to provide an introduction to distribution theory and some of its applications
Teaching style: In presence
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. PaleyWiener 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.
ANDREA BRUNO CARBONARO (President)
ADA ARUFFO
GIOVANNI ALBERTI (President Substitute)
The class will start according to the academic calendar.
Oral.