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Course, academic year 2019/2020
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Geometric Aspect of Harmonic Analysis - NRFA180
Title in English: Geometrické aspekty harmonické analýzy
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: T_KMA (18.05.2010)
There is a handful of problems in modern harmonic analysis in which the key role is played by geometry, combinatorics and probability. In this course we focus on the theory required to understand these problems and on survey of partial results. We focus in particular on Kakeya sets, directional maximal operators, Bochner-Riesz operators, restriction operators and operators with rough kernels.
Syllabus -
Last update: T_KMA (18.05.2010)

1) Review: L^p spaces, interpolation, Fourier transform,

singular operators

2) Kakeya set, Bezikovitch construction, estimates of the dimension

3) Maximal operators and almost everywhere convergence

4) Bochner-Riesz operators and maximal Bochner-Riesz operators

5) Fourier restriction and curvature

6) Operators with rough kernels

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