Fourier Analysis - Fall 2002
Office: LeConte 313 D
Office Hours: (TBD)
The course is the study of the basic principles of Fourier analysis and the necessary prerequisites for the analysis of wavelets. 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 (point-wise 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 Hardy-Littlewood maximal operator, the Riesz-Thorin and Marcinkiewicz interpolation theorems, function spaces, Riesz' theorem.
Applications will include topics in the theory of partial differential equations and signal processing, in particular the FFT.
Real Analysis (Math 703-704)
Link to Weekly Outline
Assigned Homework (50%), Mid-term exam (25%) and Final (25%).
|This page maintained by Robert Sharpley
and last updated March 26, 2002.
This page ©2001-2002, The Board of Trustees of the University of South Carolina.
Return to Sharpley's Home Page