MATH 750 Fourier Analysis  - Fall 2006 Professor Robert Sharpley Meets: TuTh  12:30-1:45 in LeConte College 310 Instructor Information  Office:   LeConte 313 D, and Sumwalt 206.  Office Hours: TuTh 1:45-3:00 and by appointment.

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 (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.

Prerequisites
  Real Analysis (Math 703-704)

Lectures:
    Link to Weekly Outline

Primary Reference

• "An Introduction to Harmonic Analysis"(3-rd ed.) by Yitzhak Katznelson, Paperback - Cambridge University Press, 2004.
  ([ISBN-13: 9780521543590 | ISBN-10: 0521543592], Call #: QA403 .K3).

Additional References

• "Interpolation of Operators," by C. Bennett and R. Sharpley, Academic Press, New York, 1988. (469 pp.) [QA3 .P8 vol. 129]
• "Fourier Series" by G. H. Hardy and Werner Rogosinski, - Paperback - Dover Pubns, 1999. (112 pp.) [QA 404 .H3 1962].

Course Grading
   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.

sharpley@math.sc.edu

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated May 6, 2006.  This page ©2006-2007, The Board of Trustees of the University of South Carolina.  URL: http://www.math.sc.edu/~sharpley/math750

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