CODE 61683 ACADEMIC YEAR 2019/2020 CREDITS 8 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 8 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian (English on demand) 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 ANDREA BRUNO CARBONARO Exam Board ANDREA BRUNO CARBONARO (President) GIOVANNI ALBERTI GIANFRANCO BOTTARO LESSONS LESSONS START The class will start according to the academic calendar. Class schedule ADVANCED ANALYSIS 1 EXAMS EXAM DESCRIPTION Oral.
