LEARNING OUTCOMES
* rigorous reasoning with Fourier series and integrals
* operating with Schwartz test functions and distributions
* recognizing applicability and connections of Fourier analysis in other parts of mathematics
Credits: 5
Schedule: 07.01.2025 - 17.02.2025
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Tuomas Hytönen
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Schwartz test functions and distributions (generalized functions)
Fourier transform of integrable and square-integrable functions, measures and distributions
Summation methods for Fourier series and integrals (Fejer means)
Fourier transform in probability theory (Lévy’s inversion theorem)
Fourier analytic description of different classes of functions (Paley-Wiener theorem)
A peek into nontrigonometric Fourier analysis (such as wavelets)
Compared to MS-C1420 and (the Fourier analysis part of) MS-C1350, this course will both fill in several details in the development of the basic theory as well as reach out to new topics.
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: lectures, exercises and exam.
Assessment methods: exercises and an exam.
Workload
valid for whole curriculum period:
contact hours 36h (no compulsory attendance)
self-study ca 100h
DETAILS
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Spring III
2025-2026 Spring III