MATH 542 - Fourier Analysis

3 units (fi 6)(EITHER, 3-0-0)

Faculty of Science

Review, theory and extension of Fourier series for square integrable functions; orthonormal systems, Bessel's inequality, completeness, Parseval's identity, Riesz-Fischer Theorem. Extension to Fourier series for functions in other Lebesgue classes; Fejer means, conjugate series, Dirichlet, Fejer and Poisson kernels. Norm convergence; remarks on pointwise convergence. Fourier transforms and series in several dimensions; inverse transform, Plancherel formula, Poisson Formula, maximal functions, Riesz-Thorin Theorem and applications. Elementary distribution theory; D, D', S, S' and some elementary results, Fourier transforms of tempered distributions. Examination of some earlier results with tempered distributions instead of functions and getting familiar with basic concepts. Prerequisite: MATH 418.

No syllabi

Winter Term 2026

Lectures

Section Capacity Class times Login to view Instructor(s) and Location
LECTURE Q1
(88928)
20
2026-01-05 - 2026-04-10 (MWF)
14:00 - 14:50