MATH 750
Fourier Analysis  Fall 2002 Office: LeConte 313 D Office Hours: (TBD) 


Course Topics
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 (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.
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 References
Additional References
Course Grading
Assigned Homework (50%), Midterm exam (25%) and Final (25%).


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