Fall 2015, Math 890, Fourier Analysis
Course Information
- This course introduces some topics in Fourier analysis on the Euclidean spaces. We will use the book by E. Stein and G. Weiss, ``Introduction to Fourier Analysis on Euclidean spaces". For background material, we recommend the book by G. Folland, ``Real Analysis: Modern techniques and their applications". We tentatively plan to cover Chapter 1, 2, 4 in Stein and Weiss' book. More precisely, the topics are 1. The L^1 and L^2 theory of the Fourier transform. 2. The Schwartz class and the tempered distributions. 3. Introduction to harmonic and subharmonic functions, and characterization of Poisson integrals. 4. The Hardy-Littleowood maximal function and boundary values of harmonic functions. 5. Spherical harmonics and a decomposition of L^2 into Fourier-invariant subspaces. 6. The Fourier transform of P(x)/|x|^{n+k-\alpha}, where 0\le \alpha< n and P(x) is a harmonic polynomial of degree k, and the principal value distributions. If time permits, we will discuss the interpolation theory of operators in L^p spaces and Lorentz spaces.
- Time: MWF 1:00 --- 1:50 PM
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- Location: Snow Hall 456
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- Text: Introduction to Fourier Analysis on Euclidean Spaces, By E. Stein and G. Weiss
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- Instructor: Shuanglin Shao
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- Office: Snow Hall 615
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- Email: slshao@ku.edu
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- Office Hour: MWF: 2:00 --- 3:00 PM, or by appointment.
Miscellaneous
There will be no exams in this course. There are 3 or 4 homework assignments throughout the course.
Homework 890.