Osion kuvaus

  • Harmonic analysis

    This is a home page of a course on harmonic analysis. The course practices will be discussed in the first lecture on Mon 9 Jan 2023. Lectures are held in M234 (M3). We have adopted a flipped classroom model for the course. The participants are expected to study the announced pages of the lecture notes before each lecture. 

    Schedule

    Mon 9 Jan: Pages 1-8 of the lecture notes.

    Thu 12 Jan: Pages 9-15 of the lecture notes.

    Mon 16 Jan: Pages 16-23 of the lecture notes.

    Thu 19 Jan: Pages 24-32 of the lecture notes.

    Mon 23 Jan: Pages 33-42 of the lecture notes.

    Thu 26 Jan: Pages 43-52 of the lecture notes. Section 3.4 on pages 48-52 can be omitted in the first reading. 

    Mon 30 Jan: Pages 53-62 of the lecture notes.

    Thu 2 Feb: Pages 63-73 of the lecture notes.

    Mon 6 Feb: Pages 74-80 of the lecture notes.

    Thu 9 Feb: Pages 81-93 of the lecture notes.

    Mon 13 Feb: Pages 94-99 of the lecture notes.

    Thu 16 Feb: Pages 100-106 of the lecture notes.

    Topics

    • Hardy-Littlewood maximal function
    • Calderon-Zygmund decomposition
    • Functions of bounded mean oscillation (BMO)
    • Marcinkiewicz interpolation theorem
    • Muckenhoupt weights
    • Singular integrals of Calderon-Zygmund type

    The learning objective of the course is to get to know modern methods in harmonic analysis. There are many challenging research topics for master's and doctoral theses. 

    Prerequisites: Participants are expected to take MS-E1281 Measure and integral before attending this course. MS-E1281 Real analysis is also recommended.

    Grading: There is no final exam. The grading is based on homework assignments and attendance. 

    Solved homework assignments      Grade

    90%                                                    5

    80%                                                    4

    70%                                                    3

    60%                                                    2

    50%                                                    1

    Instructor: Juha Kinnunen

    Course assistant: Kim Myyryläinen