Math 8370, Harmonic Analysis 1

Spring Semester 2, 2013-14

Course Lecturer

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227

Course Syllabus: For course syllabus, click here!
Course Information:
The material to be covered includes some of Chapter I and most of Chapters II, III, IV, and VI in the Katznelson book. Topics to be covered include: A review of periodic functions and T, trigonometric polynomials, and Fourier series on the circle, including convergence problems for Fourier series on T, including L^1 and L^2; mean, pointwise and absolute convergence. Convolution in L^1(T). Conjugate functions, maximal functions, and Hardy spaces. An overview of interpolation of norms and linear operators; the Hausdorff-Young theorem. The Fourier Transform in L^1(R): convolution in L^1(R) approximate identities and the Poisson summation formula. The Fourier transform in L^2(R), inversion and the Plancherel Theorem. The course will conclude with an introduction to the wavelet transform and the Haar wavelet expansion, the multiresolution analysis construction: scaling functions and wavelets, and if time permits, we will finish up with a discussion of Daubechies wavelets with compact support.

Math 5320,or 6320, or instructor consent.

Course Text:
We will use the text "An Introduction to Fourier Analysis and Wavelets" by M. Pinksy, American Math. Society, 2002 covering most of Chapters 1 - 4 and parts of Chapter 6. We will also use as references the book "An Introduction to Harmonic Analysis" by Y. Katznelson, Dover, 1976.

Assessment: Lecture Hours and Venue:
MWF 1 p.m.-1:50 p.m. ECCR 118

Office Hours:
MWF 3-4 p.m., and by appointment.

Some Important Names associated with Harmonic Analysis :
Back to the home page of Judith A. Packer
Last modified January 10, 2014.