MATH 750
Fourier Analysis  Fall 2006 Office: LeConte 313 D, and Sumwalt 206. Office Hours: TuTh 1:453:00 and by appointment. 


Course Announcements For Sunday, Sept 3, 2006:

Course Topics
The course is the study of the basic principles of Fourier analysis.
Lectures will drawn from several references (listed below) and
will include the following topics:
Fourier series of periodic functions and the Fourier transform on the line: representation of functions, i.e. convergence and divergence (pointwise sense, in the norms of various function spaces, and almost everywhere), convergence of Fejer means and summability; Parseval's relation and the square summable theory; conjugate Fourier series, the conjugate function and the Hilbert transform, the HardyLittlewood maximal operator, the RieszThorin and Marcinkiewicz interpolation theorems, function spaces, Riesz' theorem. Additional topics may include Poisson summation formula, unconditional convergence of Fourier series; introduction to Fourier multipliers and wavelets.
Applications will include topics in the theory of partial differential equations and signal processing, in particular the FFT.
Prerequisites
Real Analysis
(Math 703704)
Lectures:
Link to Weekly Outline
Primary Reference
Additional References
Course Grading
Assigned Homework (50%), Midterm exam (25%) and Final (25%).
Homework Assignments & Other Course Materials
Check this Link for homework
assignments and other course materials.


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and last updated May 6, 2006. This page ©20062007, The Board of Trustees of the University of South Carolina. URL: http://www.math.sc.edu/~sharpley/math750 