Fachbereich Mathematik 
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Seminar on Selected Topics in Harmonic Analysis (WiSe 19/20)

Seminar dates (first meeting on October 17th): Thursday, 14-16, Room 415.

Credits : 6 ECTS (given on the base of the oral presentation and a written report on the chosen topic).

List of possible topics:
  • Riesz-Thorin interpolation theorem with applications and extensions to analytic families of operators (Turan Can)
  • Lorentz spaces and interpolation: main properties, normability and the off-diagonal Marcinkiewicz interpolation theorem (Döpp Sophie)
  • Convolution and approximate identities in locally compact groups (Shenas Sofia)
  • BMO and the extension of Calderón-Zygmund operators to L^infty (Funk Martin)
  • Oscillatory integrals, the Van der Corput lemma and the stationary phase method (Aydin Umut)
  • Decay estimates for Fourier transforms of measures
  • Restriction estimates for the Fourier transform
  • Bessel Potentials and general Sobolev spaces (Schmeckpeper Dennis)
  • The Littlewood-Paley decomposition and an alternative characterization of general Sobolev spaces
For a detailed description, consult the following file.

Dates of the seminars:
  • Friday, December 13, 14:00-16:00, room 432: Turan, Funk.
  • Wednesday, December 18, 16:00-18:00, room 432: Shenas, Aydin.
  • Thursday, December 19, 14:00-16:00, room 415: Döpp, Schmeckpeper.
  • Javier Duoandikoetxea, Fourier Analysis, Graduate Studies in Mathematics, 29, American Mathematical Society, 2001.
  • Loukas Grafakos, Classical Fourier Analysis, Third Edition, Springer, 2014.
  • Loukas Grafakos, Modern Fourier Analysis, Third Edition, Springer, 2014.
  • Elias M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.
  • Elias M. Stein, Timothy S. Murphy, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Vol. 3. Princeton University Press, 1993.
  • Elias M. Stein, Guido Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.

  Seitenanfang  Impress 2019-12-13, Seminar Harmonic Analysis