Politecnico di Torino
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Politecnico di Torino
Anno Accademico 2007/08
02GPVKY
Functional analysis
Corso di L. Specialistica in Ingegneria Elettronica (Electronic Engineering) - Torino
Docente Qualifica Settore Lez Es Lab Tut Anni incarico
SSD CFU Attivita' formative Ambiti disciplinari
MAT/05 5 C - Affini o integrative Cultura scientifica, umanistica, giuridica, economica, socio-politica
Obiettivi dell'insegnamento
The aim of the course is to present the theory of vector spaces in infinite dimensions, and analogues of well-known results in matrix and linear algebra. Particular attention will be given to the study of completeness and Hilbert spaces, including applications to the convergence of Fourier series. Along the way, the course will provide an introduction to some of the spaces of functions used in analysis.
Prerequisiti
A good grounding in linear algebra and basic analysis, especially the definition of limits, convergence and continuous functions.
Programma
Normed linear spaces; convexity; inequalities
Sequences of numbers and continuous functions
Convergence and completeness; basic topology
Spaces of integrable functions (without technical detail)
Hilbert spaces; examples and applications
Orthogonality, projections and minimal distance
Bounded operators; the dual space
Self-adjoint operators; elementary spectral theory
Laboratori e/o esercitazioni
Supervised sessions of problem solving.
Statistiche superamento esami

Programma definitivo per l'A.A.2007/08
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