Alcune Note di Analisi Matematica

Preprint Italian OPEN
Vasselli, Ezio;
(2011)
  • Related identifiers: doi: 10.13140/RG.2.1.5017.4569/1
  • Subject: Mathematics - Operator Algebras | Mathematics - Classical Analysis and ODEs | Mathematics - History and Overview

Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
  • References (3)

    7 Analisi Funzionale. 106 7.1 Spazi di Banach e di Hilbert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.2 Operatori limitati e C∗-algebre. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.3 Uniforme limitatezza ed applicazioni aperte. . . . . . . . . . . . . . . . . . . . . . . . 118 7.4 Il teorema di Hahn-Banach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.5 Operatori compatti ed il Teorema di Fredholm. . . . . . . . . . . . . . . . . . . . . . 121 7.6 I teoremi di Stampacchia e Lax-Milgram. . . . . . . . . . . . . . . . . . . . . . . . . 125 7.7 Teoria spettrale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.8 Topologie deboli e spettri di algebre di Banach. . . . . . . . . . . . . . . . . . . . . . 133 7.9 Cenni su spazi localmente convessi e distribuzioni. . . . . . . . . . . . . . . . . . . . 139 7.10 Operatori non limitati. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.11 Il Teorema di Schauder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.12 Esercizi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

    8 Analisi di Fourier. 166 8.1 Serie di Fourier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.2 La trasformata di Fourier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.3 Esercizi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

    9 Analisi Complessa. 181 9.1 Funzioni olomorfe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 9.2 Serie di potenze e funzioni analitiche. . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9.3 Integrazione complessa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 1 dz = 1 · (ζ − ζ′) dt = ζ − ζ′ . 1 kz

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