Fourier Analysis - Fall 2006
Office: LeConte 313 D, and Sumwalt 206.
Office Hours: TuTh 1:45-3:00 and by appointment.
Course Announcements For Sunday, Sept 3, 2006:
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 (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. 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.
Real Analysis (Math 703-704)
Link to Weekly Outline
([ISBN-13: 9780521543590 | ISBN-10: 0521543592], Call #: QA403 .K3).
Assigned Homework (50%), Mid-term exam (25%) and Final (25%).
Homework Assignments & Other Course Materials
Check this Link for homework assignments and other course materials.
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