Real Analysis
C.L. in Matematica
Universita' di Milano - Anno Academico 2017/2018
Proff. K. R. Payne e L. Vesely
Preliminary syllabus (programma
preliminare) (file rtf)
Final detailed syllabus (programma d'esame) (file .pdf) (Available towards the end of the course)
ANNOUNCEMENTS:
1.
Homework Results.
a.
HW1
b.
HW2
c.
HW3 (version of 28 February)
2.
Prossime prove orali:
a.
Marted́ 19 giugno:
9.30-14.30 in Aula 6 (Studenti che
intendono presentarsi sono pregati di confermare la presenza entro Domenica 17 giugno tramite e-mail al Prof. Payne)
b.
Marted́ 17 luglio:
9.30-14.30 in Aula 6 (Studenti che
intendono presentarsi sono pregati di confermare la presenza entro Domenica 15 luglio tramite e-mail al Prof. Payne)
Office
hours (ricevimento studenti): Monday and Thursday 11.30 – 12.30 and by
appointment.
Teaching
materials:
Corse notes: These will be updated during the course, but
for now here is the link to an old version that covers the first two chapters
of the course.
1.
Differentiation and Integration + Lp spaces (K. Payne, in Italian)
2.
Hilbert Spaces (K. Payne, in English)
a.
Lectures 16 & 17 (Hilbert spaces, orthogonality, the
Projection Theorem, duality, Riesz Representation
Theorem, Lax Milgram Theorem)
b.
Lectures 18 & 19 (Orthonornal
systems, orthonormal bases, separablity, bounded
linear operators, adjoint operators, compact
operators)
c.
Lectures 20 & 21 (The Spectral Theorem, pointwise
convergence of Fourier series, summability kernels,
Riemann-Lebesgue Lemma)
Homework
assignments:
1. Homework N.1 – due date is Thursday, November 9.
2. Homework N.2 – due date is Tuesday, December 19. (New Version of December
11)
3. Homework N.3 – due date is Monday, January 22.
Old
exercizes from past years: Raccolta di
Esercizi di Analisi Reale, Parte I
(in Italian)