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Analysis course descriptions

MATH 541: Harmonic Analysis I: A first course in harmonic analysis on Euclidean spaces. Topics include:

  • Fourier series, their summability and convergence
  • The Fourier transform on the line
  • Fourier inversion, Plancherel formula, Hausdorff-Young inequality
  • The Poisson summation formula
  • The uncertainty principle
  • The stationary phase method
  • The Hilbert transform
  • The Riesz and Kolmogorov theorems
  • Lp convergence of the Fourier transform

MATH 542: Harmonic Analysis II. Continuation of MATH 542. Includes more advanced topics in harmonic analysis on Euclidean spaces, such as:

  • Maximal functions and differentiation theorems
  • Kakeya sets and the Kakeya maximal function
  • The Tomas-Stein theorem and restriction estimates
  • Fourier transforms of singular measures
  • Applications to geometric measure theory: convolutions, projections, distances
  • Variants of the Hilbert transform

MATH 543: Discrete Harmonic Analysis Introduction to discrete harmonic analysis and additive number theory. MATH 543 was only recently added to the UBC calendar and has not yet been taught under that name, but it will be similar to MATH 613 (Fall 2011). Topics include:

  • Discrete Fourier transform
  • Roth's theorem on 3-term arithmetic progressions
  • Freiman's theorem
  • Quadratic uniformity and Szemeredi's theorem on 4-term arithmetic progressions

 

a place of mind, The University of British Columbia

Mathematics Department

Harmonic Analysis Research Group
1984 Mathematics Road
Vancouver, B.C. Canada V6T 1Z2
Tel: 604-822-2666
Fax: 604-822-6074
E-mail: info@harmonic.math.ubc.ca

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