Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Mo, Fr 11:15 in Research I, 107 |
Grader: | Mahmut Çalik |
Email: | m.calik@jacobs-university.de |
Lectures: | We 11:15, Fr 9:45 in East Hall 3 |
Homework: | 30% |
Midterm Exam: | 30% |
Final Exam: | 40% |
03/09/2008: | Motivation, sigma-algebras, measures |
08/09/2008: | Construction of the Lebesgue measure I: From outer measure to measure |
10/09/2008: | Construction of the Lebesgue measure II: From pre-measure to outer measure; monotone class theorem, uniqueness of measures |
15/09/2008: | Measurable functions and integrals |
17/09/2008: | Monotone convergence, Fatou's lemma, dominated convergence |
22/09/2008: | Product measures, Fubini-Tonelli theorem |
24/09/2008: | Proof of the Fubini-Tonelli theorem; Layer cake representation |
29/09/2008: | Normed spaces, L^{p}-spaces, Jensen's inequality |
01/10/2008: | More inequalities: Young, Hölder, Minkowski, Hanner |
06/10/2008: | Completeness of L^{p}; Bounded linear functionals on Banach spaces, dual space, weak convergence |
08/10/2008: | uniform boundedness principle |
13/10/2008: | Dual of L^{p} |
15/10/2008: | Convolution, mollifiers, separability of L^{p} |
20/10/2008: | Midterm review |
22/10/2008: | Midterm Exam |
27/10/2008: | Midterm discussion |
29/10/2008: | Approximation by "really simple functions", separability of L^{p} |
03/11/2008: | Convolution, convergence of a mollifying sequence in L^{p} |
05/11/2008: | Banach-Alaoglu for L^{p}, Hilbert spaces (begin) |
10/11/2008: | Hilbert spaces |
12/11/2008: | Fourier Transform |
17/11/2008: | Fourier Transform |
19/11/2008: | Fourier series, pointwise convergence of Fourier series for continuous functions of bounded variation |
24/11/2008: | Stone-Weierstrass Theorem |
26/11/2008: | Distributions |
28/11/2008: | Distributions |
03/12/2008: | Review for final exam |
18/12/2008: | Final Exam, 16:00-18:00 in Research II Lecture Hall |