schedule.
The lectures will be given on Zoom.

(The last lecture has now been given.)

**Course literature:**

G. B. Folland: "Real Analysis" (selected chapters).

Chapter 8.1 in Elias M. Stein, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals"
(see JSTOR).

M. Einsiedler and T. Ward, "Ergodic theory with a view towards number theory" (selected sections).

Some course notes.

**Examination:**

Three assignments will be given during the course. For each assignment one can get
0-100 points. To pass the course, one has to submit solutions to all three assignments, have at least 20 points on each
of them and at least 100 points altogether.

assignment #1 (due October 6, before midnight)

- some comments & answers.

assignment #2 (due November 12, before midnight)

- some comments & answers.

assignment #3 (due December 17, before midnight)

- some references.

**Preliminary plan**:

1. Sums and integrals (Sec. 1 in the course notes)

2. Measure and integration theory (~ Folland Ch. 1.1-1.3)

3. Measure and integration theory (~ Folland Ch. 2.1-2.3 and 2.5-2.7; Sec. 2 in the course notes)

4. Measure and integration theory (~ Folland Ch. 3.1-3, 6.1-2, 7.1-3; Sec. 3 in the course notes)

5. Convolution (~ Folland Ch. 8.2)

6. The Fourier Transform (~ Folland Ch. 8.3; Sec. 4 in the course notes)

7. More on Fourier analysis (~ Folland Ch. 8.3 and 8.6)

8. Positive integrals; the gamma function (Sec 7 in the course notes)

9. The J-Bessel function (Sec 8 in the course notes)

10. Stationary phase (Stein Ch. 8.1)

11. Stationary phase; examples (Stein Ch 8.1; Sec 9 in the course notes)

12. Distribution theory (~ Folland Ch. 9.1-2)

13. Distribution theory (~ Folland Ch. 9.1-2)

14. Tempered distributions (~ Folland Ch. 9.2)

15. Sobolev spaces (~ Folland Ch. 9.3)

16. Dynamical systems: some examples; continued fractions and the Gauss map.
(~ Ch. 3 in Einsiedler and Ward: "Ergodic theory with a view towards Number Theory")

17. Dynamical systems: some more examples.

Andreas Strömbergsson, e-mail: astrombe@math.uu.se