Project 4

Topics in Partial Differential Equations

Wilhelm Klingenberg

Description

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis lies at the heart of many areas in pure and applied mathematics. In term one, the students will write some of the fundamental concepts such as the continuous-time Fourier transform, Parseval identity (Plancherel theorem). In term 2, the students would proceed with a specialized topic such as Shannon's sampling theorem, the Weyl-Heisenberg uncertainty principle or compressed sensing.

Pre - and corequisites

AMV II, Complex Analysis II, Analysis IV

Resources

  • Stein, E.M., and G. Weiss (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press.
  • H. Dym, H.P. McKean : Fourier Series and Integrals, Academic Press 1974
  • Katznelson, Yitzhak (1976). "An introduction to harmonic analysis" (Second corrected ed.). New York: Dover Publications,

Links

email: Wilhelm Klingenberg

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