The course lies in Blok 1A. The teaching period is from August 25 to October 31, in all 9 weeks.
There will be lectures Monday 15.15-17 (Aud 9), Thursday 10.15-12 (Aud 9), 13.15-14 (Aud 8). In the week September 8-12 there will be no lectures because I will participate in an international conference on orthogonal polynomials in Spain. You are supposed to work with the first set of exercises out of 3. They shall be handed in at the following dates: September 15, October 6 and October 27. The grading (pass/nonpass or following the 7-level scale) will depend on your choice. You should decide this when you hand in the first set of excercises, and then it cannot be changed.
Problems for September 15: Problem set I
Problems for October 6: Problem set II
Problems for October 27: Problem set III
Week 35: Introduction and 2.1. You should browse through Chapter 1: The main result is the Riesz representation theorem 1.2.2, which establishes a one-to-one correspondence between Radon measures and positive linear functionals. The notion of support of a Radon measure is also important (section 1.3) as well as the section 1.4 on vague and weak convergence.
Week 36: 2.2 and 2.3.
week 37: No lectures
week 38: 2.4 and 2.5. I finished at the end of page 71.
week 39: The rest of 2.5 and 2.6.
week 40: On Monday I finished the last 3 pages of 2.6 and handed out 8 pages about Hermite and Laguerre polynomials. I began lecturing on Hermite polynomials and will finish these pages on Thursday and probably also begin to lecture about Jacobi polynomials. For this I will find some additional material. It is good to know that all the orthogonal polynomials can be found on the website orthogonal polynomials This website contains many systems we did not discuss. The classical ones are also available at Maple. You can download the worksheet ortopol.mw by saving it as worksheet and take it into maple. ortopol.mw
week 41: I hand out some pages about the classical orthogonal polynomials which complements the previous handout. I will lecture on section 2.7. Of the two proofs of Theorem 2.7.7 I only lectured on the second due to Barry Simon. On page 100, line 8 where a formula for h_0(u,v) is given, the lower left corner of the matrix shall be (v-u)P_0^2 instead of (v-u). I formulated Theorem 2.7.11 but will return to the proof in week 43.
week 42: Official vacation
week 43: The lecture on Monday 20 was cancelled because of illness. On Thursday I finished essentially section 2.7 and started on 2.8, proving Naimark's theorem. I also gave an overview about orthonormal systems in an abstract Hilbert space, thus formulating Lemma 2.8.4 in a general context.
week 44: I lectured on section 2.8 and ended with formulating Proposition 2.8.14. On Thursday I will say a little about several variables from 2.8 and prove Carlemans theorems from section 2.9.