KTH
Matematik
SF2705, Fourieranalys, 2011/2012.SF2705, Fourier Analysis, 2011/2012.7.5 hpoängLiterature:E. M. Stein, R. Shakarchi, Fourier analysis. An introduction. Princeton Lectures in Analysis, 1. Princeton University Press, Princeton, NJ, 2003.Course contentWe 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 issuesThe course ends with an oral examination. Date: Tuesday May 8, 2012, at 11:00.Till Håkan Hedenmalms hemsida. Course beginsThe course begins on Thurday, Feb. 2, at 13.15 in room 3721. Observe the altered date!!! We will initially meet on Thursdays 13-15 and Fridays 15-17 in room 3721. Suggested problems: pp. 58-66: 1, 2, 5, 7, 10, 11, 12, 13, 15, 16 pp. 65-67: 1, 2 pp. 87-94: 2, 3, 7, 9, 13, 14, 15, 16, 17 pp. 95-99: 1, 2, 3, 4, 5. pp. 120-125: 1, 2, 3, 4, 5, 6, 8, 9, 10 pp. 125-128: 1, 2, 3, 4 pp. 161-169: 1, 2, 3, 4, 12, 13, 14, 15, 16, 17, 18, 19, 23 pp. 207-212: 1, 2, 3, 4, 5, 6, 7, 8 pp. 275-279: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 | |
|
|
Uppdaterad: 2011-12-02