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PMATH 454Fourier Analysis

Units
0.50
Faculty
Mathematics
Subject
Pure Mathematics

When it runs

  1. F24
  2. W25
  3. S25
  4. F25
  5. W26
  6. S26
  7. F26
  8. W27
  9. S27

Ran in 1 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.

Fourier analysis on the circle: Fourier series; Hilbertian analysis; convolutions and summability kernels; Pointwise, uniform and Lp convergence of Fourier series. Fourier analysis on the real line: test and Schwarz class functions, distributions and tempered distributions, Fourier transforms, inversion theorem, L1 and L2 analysis. Selected applications.

Prerequisites

  • Must have completed the following:

Antirequisites

None listed.

Leads to

No course lists it as a requisite.

Winter 2027 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 00163350 / 25MWF 16:30–17:20
LEC 701240914 / 9999Online or by arrangement

Reviewed on UW Flow

100% liked it0% easy75% useful

From 3 ratings and 2 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • Very interesting material and a fun combination of a lot of analysis one sees throughout the years, though the two halves of the course (Fourier series and the Fourier transform) felt rather disjoint and not very well-motivated what they had to do with each other besides similar vibes. Relies on the prerequisites very heavily.

    Apr 2026 · liked itOn UW FlowRemove this

  • The course was split into two parts. The first was about Fourier series and the second was on Fourier transforms. This was a very high amount of content, and thankfully the midterm and final covered only the first and second half of the content respectfully. The assignments were all very difficult and I needed to spend a lot of time on them. Even then I didn't do very well.
    The motivation behind why we care about Fourier transforms and series was not covered in much detail. If you accept the need to study them as a fact (or just like learning new math), then everything else in the class was very well motivated. For my offering, I felt that an in-depth story on summability kernels, the…

    Apr 2026 · liked itOn UW FlowRemove this

Check it elsewhere for Fall 2026

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