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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:
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Riesz-Thorin interpolation theorem with applications and extensions to analytic families of operators (Turan Can)
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Lorentz spaces and interpolation: main properties, normability and the off-diagonal Marcinkiewicz interpolation theorem (Döpp Sophie)
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Convolution and approximate identities in locally compact groups (Shenas Sofia)
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BMO and the extension of Calderón-Zygmund operators to L^infty (Funk Martin)
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Oscillatory integrals, the Van der Corput lemma and the stationary phase method (Aydin Umut)
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Decay estimates for Fourier transforms of measures
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Restriction estimates for the Fourier transform
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Bessel Potentials and general Sobolev spaces (Schmeckpeper Dennis)
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The Littlewood-Paley decomposition and an alternative characterization of
general Sobolev spaces
For a detailed description, consult the following
file.
Dates of the seminars:
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Friday, December 13, 14:00-16:00, room 432: Turan, Funk.
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Wednesday, December 18, 16:00-18:00, room 432: Shenas, Aydin.
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Thursday, December 19, 14:00-16:00, room 415: Döpp, Schmeckpeper.
Literature:
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Javier Duoandikoetxea, Fourier Analysis, Graduate Studies in Mathematics, 29, American
Mathematical Society, 2001.
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Loukas Grafakos, Classical Fourier Analysis, Third Edition, Springer, 2014.
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Loukas Grafakos, Modern Fourier Analysis, Third Edition, Springer, 2014.
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Elias M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.
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Elias M. Stein, Timothy S. Murphy, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Vol. 3. Princeton University Press, 1993.
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Elias M. Stein, Guido Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.