Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMA300F valid from Spring 2015

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  • English
  • If sufficient demand
  • To make the participants acquainted with the theory of Riesz products which constitute a usefool tool for research in mathematical analysis. Among other things they have been used to give examples of continuous, nowhere differentiable functions and of periodic functions, the Fourier coefficients of which decay as slowly as for typical piecewise continuous functions with discontinuities.
  • Construction of Riesz products on different groups (in particular S^1);
    Basic properties;
    Random Riesz products;
    Almost everywhere convergence of lacunary Fourier series;
    Applications to Diophantine approximation and multifractal analysis of some ergodic averages.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to account for the construction of Riesz products.
    Be able to give examples of applications to the theory of dynamical systems.
Competences and Skills
  • For a passing grade the doctoral student must
  • Be able to use Riesz products to construct functions with desired “exotic” properties.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
Examination Formats
  • Written exam
  • Oral exam
  • Take-home exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • Integration Theory, Fourier Analysis, Nonlinear Dynamic Systems
Selection Criteria
  • Lecture notes will be provided.
Further Information
Course code
  • FMA300F
Administrative Information
  •  -04-18
  • FN1/Anders Gustafsson

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