Coordinator: Prof. Antonio Vicino
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Functional Analysis And Applications


Andrea Mennucci
Scuola Normale Superiore
Course Type
Type A
May 27 h. 10-13 Aula 8; h. 16-18 Aula 13
May 28 h. 10-13 Aula 21; h. 15-17 Aula 21
May 29 h. 10-13 Aula 21; h. 17-19 Aula 13
May 30 h. 11-14 Aula 13; h. 16-18 Aula 8
May 31 h. 9-11 Aula 13; h. 15-17 Aula 13
Hilbert spaces: Hilbert projection Theorem, Bessel inequality, Parseval equality, Riesz-Fischer Theorem.
Fourier Series (FFT), cosine series.
Elements of discrete wavelet transforms (DWT).
Fourier transform.
Elements of topological vector spaces.
Distributions, tempered distributions.
Fourier transform and distributions.
Signal analyis: sampling, Shannon base, Nyquist Theorem, Gibbs phenomenon.
Applications to analysis of sounds and images, using FFT and DWT; theory and numerical applications.

[1] Rudin, Real and Complex Analysis, McGraw–Hill, 1987.
[2] Rudin, Functional Analysis
[3] Stéphane Mallat, "A wavelet tour of signal processing, the sparse way", Academic Press



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