Each student will learn the basic concepts and properties both of the theory of linear operators on Hilbert spaces and of that of distributions.
Course Prerequisites
It is assumed that the students masters the content of all courses, given during the first two years of the batchelor studies in physics.
Teaching Methods
All classes will be given at the blackboard
Assessment Methods
Both a written and an oral exam will verify the student mastership of the subject. Particular emphasis will be given to the abilty of exposing the concepts with mathematical rigour and appropriate methodology.
Texts
1. V. Moretti, "Teoria Spettrale e Meccanica Quantistica" (2010) Springer
2. G. Friedlander & S. Joshi, "Introduction to the Theory of Distributions", 2nd ed. (1999) Cambridge University Press
Contents
During the first part of the course, the theory of linear operators on Hilbert spaces will be introduced. As far as bounded operators are concerned, great emphasis will be given to the study of compact, Hilbert-Schimdt and trace class operators. In the general cases we will focus mainly on self-adjoint and essentially self-adjoint operators. as well as on their physical applications. To conclude the basics of spectral theory will be outlined.
During the second part of the course, we will present the theory of distributions, especially those tempered and of compact support. The main operations between distributions as well as the key applications, such as the theory of convolutions and Fourier transforms, will be explained. If time allows, more recent concepts, such as that of wavefront set, will be introduced.
Course Language
Italian
More information
All students who are entitled to benefit from the inclusive teaching methods (see portale.unipv.it/it/didattica/servizi-lo-studente/modalita-didattiche-inclusive) will be given access to the lecture notes and to the videos available on KIRO. Furthermore, they are cordially invited to contact the chair of the course to set up online meetings or group activities.
