SF2705, Fourieranalys, 2011/2012.
SF2705, Fourier Analysis, 2011/2012.
7.5 hpoäng
Literature: E. M. Stein, R. Shakarchi, Fourier analysis.
An introduction. Princeton Lectures in Analysis, 1.
Princeton University Press, Princeton, NJ, 2003.
Course content
We cover the basics of Fourier series, involving the Dirichlet and Fejer
kernels, Dini's test, etc. We
will discuss the Lebesgue integral as well because it helps to understand
the topic. We also apply the results to e.g. Weyl's equidistribution theorem.
Then we do Fourier analysis on the real line, and mention extensions to higher
dimensions. We discuss Fourier analysis on finite abelian groups, and apply
the results in the setting of Dirichlet characters to obtain Dirichlet's
famous theorem on the distribution of primes in arithmetic progressions.
Examination issues
The course ends with an oral examination. Date: Tuesday May 8, 2012, at
11:00.
Till Håkan Hedenmalms hemsida.
Course begins
The course begins on Thurday, Feb. 2, at 13.15 in room 3721. Observe
the altered date!!!
We will initially meet on Thursdays 1315 and Fridays 1517 in room 3721.
Suggested problems:
pp. 5866: 1, 2, 5, 7, 10, 11, 12, 13, 15, 16
pp. 6567: 1, 2
pp. 8794: 2, 3, 7, 9, 13, 14, 15, 16, 17
pp. 9599: 1, 2, 3, 4, 5.
pp. 120125: 1, 2, 3, 4, 5, 6, 8, 9, 10
pp. 125128: 1, 2, 3, 4
pp. 161169: 1, 2, 3, 4, 12, 13, 14, 15, 16, 17, 18, 19, 23
pp. 207212: 1, 2, 3, 4, 5, 6, 7, 8
pp. 275279: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16


