Institut für Mathematik

Vorlesungen/Details

MAT610
Harmonic Analysis
https://www.math.uzh.ch/fileadmin/user/pid_32674/bilder/252456-250652_Foto_Widmayer.jpg
Prof. Dr. Klaus Widmayer

Vorlesungen

Di
Zeitraum:
10:15 - 12:00
Raum:
Y27H12 Plätze: 50

Review of topics

  • Week 1: Introduction/Historical Background. Fourier series on the torus. Basic properties of Fourier coefficients (Riemann-Lebesgue lemma). Partial sums and the Dirichlet kernel. Criteria for pointwise convergence (Dini).
  • Week 2: Partial sums and continuity (duBois-Reymond). Summability methods: Fejér and Poisson kernels. Approximate identities. Density of trigonometric polynomials in L^p.
  • Week 3: Norm convergence of partial sums: L^2 setting. Relation to boundedness of partial summation. The Maximal function: introduction and basic properties.
  • Week 4: Weak L^1 and L^p boundedness of the maximal function
  • Week 5: The maximal function and a.e. convergence of radially bounded approximate identities
  • Week 6: Weak L^p spaces, maximal operators and a.e. convergence, Marcinkiewicz interpolation
  • Week 7: Fourier transform, Schwartz space
  • Week 8: Tempered distributions and their Fourier transform
  • Week 9: Hilbert transform

VVZ Link