Functional analysis, spring 2006 (för Matnat, fristående kurs, F3B).

web-page: http://www.math.uu.se/~astrombe/FA2006/FA2006.html

Teacher: Andreas Strömbergsson email: firstname.lastname at math dot uu dot se (with "o" in place of "ö").

NEW EXAM 4p: 17 August, 9-14, Polacksbacken. (Those of you who wish to do exam for 6p, please contact me on email to set time for further examination!)

NEW EXAM 4p: 12 June, 9-14, Polacksbacken. (Those of you who wish to do exam for 6p, please contact me on email to set time for further examination!)

Exam 21 April with solutions. Results.

Exam 17 March with solutions. Some results.

Literature: Kreyszig: Introductory Functional Analysis with Applications, John Wiley & Sons, New York 1989.
Also: Short text on the spectral theorem for compact self-adjoint operators.
The following text may also be helpful: Mathematical statements and proofs.
Curriculum (some small changes are possible!): For 4 points. For 6 points.

Homework assignments: These may result in up to 6 bonus points on the exam. In precise terms: x % on the homework assignments give x/10-3 (rounded downwards to nearest integer) bonus points (if 30 <= x < 100). The three assignments, and deadlines for returning, are:

Homework assignment 1 -- now with solutions, 10 February (all 6 problems).
Homework assignment 2 -- now with solutions to ALL problems., 24 February. For 6p, problems 5,6: 13 March.
Homework assignment 3 -- now with solutions to ALL problems, 15 March. For 6p, problems 5,6: 18 April.

Lectures (all lectures are at Polacksbacken):

Day Time Room Sections Subject
1: Tue, 24 Jan 8-10 1_113 Ch. 1 Introduction, metric spaces
2: Thu, 26 Jan 8-10 1_113 Ch. 1 Metric spaces
3: Tue, 31 Jan 13-15 1_113 Ch. 1 PROBLEM SOLVING (1.2: 4,6,8,10,11. 1.3: 1,6,10,12,13. 1.5: 2,3,10. 1.6: 8,12)
4: Wed, 1 Feb 8-10 1_113 Ch. 2 Normed spaces, Banach spaces
5: Thu, 2 Feb 15-17 1_113 Ch. 2 Normed spaces, Banach spaces
6: Fri, 3 Feb 10-12 1_113 Ch. 2 PROBLEM SOLVING (2.2: 11,15. 2.3: 1,2,3,6,8. 2.4: 1,3,8. 2.5: 1,3,9. 2.6: 13,14,15)
7: Mon, 6 Feb 10-12 2_244 Ch. 2 Normed spaces, Banach spaces
8: Wed, 8 Feb 8-10 1_113 Ch. 3 Inner product spaces, Hilbert spaces
9: Thu, 9 Feb 8-10 1_113 Ch. 2,3 PROBLEM SOLVING (2.7: 6,14. 2.8: 9,11. 2.9: 12. 2.10: 6,13. 3.1: 3,15. 3.2: 8,10. 3.3: 1,6,9. 3.4: 4.)
10: Fri, 10 Feb 10-12 1_113 Ch. 3 Inner product spaces, Hilbert spaces
11: Mon, 13 Feb 8-10 1_113 Ch. 3 Inner product spaces, Hilbert spaces
12: Wed, 15 Feb 10-12 2_244 Ch. 3 PROBLEM SOLVING (3.5: 7,9. 3.6: 6,9,10. 3.9: 6,8,10. 3.10: 4,6,9,15.)
13: Wed, 15 Feb 13-15 1_113 Ch. 4 Fundamental theorems for normed spaces
14: Fri, 17 Feb 10-12 2_244 Ch. 4 Fundamental theorems for normed spaces
15: Tue, 21 Feb 8-10 1_113 Ch. 4 PROBLEM SOLVING (4.2: 5,8. 4.3: 11,13,15. 4.6: 9,10.)
16: Wed, 22 Feb 10-12 1_113 Ch. 4 Fundamental theorems for normed spaces
17: Fri, 24 Feb 10-12 1_113 Ch. 4.8-9; 7.1-2 convergence concepts, spectral theory
18: Tue, 28 Feb 8-10 1_113 Ch. 4,7 PROBLEM SOLVING (4.7: 5,6,14. 4.8: 1,4,5. 4.9: 4,5. 7.2: 5,7,8.)
** 19: Fri, 3 Mar 10-12 1_113 Ch. 4.4-5, 4.12-13 ONLY 6p! More fundamental theorems for normed spaces
20: Wed, 8 Mar 13-15 1_113 8.1 + handout text Compact operators, spectral theory in Hilbert spaces
21: Mon, 13 Mar 8-10 1_113 Ch. 4,8 PROBLEM SOLVING (8.1: 2,4,6,8. + exercises in handout text + old exams?)
22: Wed, 15 Mar 13-15 1_113 REPETITION (solving old exams?)
Exam: 17 March.

For 6p the course continues:
 23: Wed, 22 Mar 8-10 2_215 Ch. 9 Spectral theory in Hilbert spaces 24: Wed, 29 Mar 8-10 2_215 Ch 9,10 Spectral theory in Hilbert spaces 25: Wed, 5 Apr 8-10 2_215 Ch 10.1-3 Spectral theory in Hilbert spaces. End of lecture 5 April. 26: Wed, 19 Apr 8-10 2_215 4,9,10 Prespectives (Ch 8,10,11?), or PROBLEM SOLVING (4.12: 5,7. 4.13: 5,8,15. 9.1: 7,8,9,10. 9.2: 7. 9.5: 8,10. 9.6: 8,9,10,11,12. 9.9: 5,6,7,10. 10.1: 1,2,5,8,9. 10.2: 4,6,9. 10.3: 5,7,10) Or old exam problems?
Second exam (for 6p): 21 April, kl 9.00-11.30.