S4B1 - Graduate Seminar on Analysis - Harmonic Analysis (winter term 2017/2018)
Instructor:
Dr. Błażej Wróbel
Date:
Contents:
In this seminar we will survey various results from both classical and modern harmonic analysis. Some emphasis will be put on dimension-free estimates and sharpness of the constants.
Bibliography:
- Loukas Grafakos, Classical Fourier Analysis, Graduate Texts in Mathematics Volume 249 (2008)
- Javier Duoandikoetxea, Fourier Analysis, Graduate Texts in Mathematics Volume 29 (2001)
Requirements:
List of seminar topics
- Introduction: definition of the Fourier transform and its basic properties (Inversion formula, Plancherel formula, etc.).
- Tempered distributions.
- Basics of interpolation of Lp spaces. The Marcinkiewicz and the Riesz-Thorin interpolation theorems.
- Hilbert transform.
- Calderón-Zygmund theory. Dimension-free estimates for the Riesz transforms.
- Hardy-Littlewood maximal operator. Dimension-free estimates in the ball case.
- Convolution operators and multiplier operators. Multiplier theorems.
- Fefferman's counterexample for the ball multiplier problem and the Bochner-Riesz multipliers.
- Spectral theorem and spectral multipiers.
- Basics of the theory of strongly continuous semigroups.
- Symmetric contraction semigroups. The Lp boundedness of their maximal functions.
- Semigroups with Gaussian bounds and spectral multiplier theorems.
- Dimension-free estimates in harmonic analysis 1.
- Dimension-free estimates in harmonic analysis 2.
News
ERC Consolidator Grant for Dr. Evgeny Shinder
Jessica Fintzen wins Cole Prize
Vacancy: Office employee (Application deadline: 3.12.23)
Dr. Regula Krapf receives university teaching award
Prof. Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Prof. Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Prof. Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Rajula Srivastava receives Association for Women in Mathematics Dissertation Prize
Prof. Ana Caraiani wins a New Horizons in Mathematics Prizes 2023
Pius XI Medal awarded to Professor Peter Scholze
Prof. Valentin Blomer und Prof. Georg Oberdieck erhalten ERC grants
Grants for Mathematics students from Ukraine
Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant