|CREDITS||8 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA|
|SCIENTIFIC DISCIPLINARY SECTOR||MAT/05|
|TEACHING LOCATION||GENOVA (Mathematics)|
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. 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.
ANDREA BRUNO CARBONARO (President)
GIOVANNI ALBERTI (President Substitute)
The class will start according to the academic calendar.