Instructor: P. Sacks                                     Office: 436 Carver

Telephone: 294-8143                                  E-Mail: psacks@iastate.edu

Class Web page: www.public.iastate.edu/~psacks/classes/m690H/math690H.html

Office Hours: Monday, Friday 1-2, Wednesday 10-11 or by appointment

Course Content: This course will cover the classical theory of Fourier series and the Fourier transform, with applications as time permits.

• Fourier series of periodic functions: Fourier series of functions from various function spaces, norm and pointwise convergence, Gibbs phenomenon, summability methods, approximation by trigonometric functions
  
• Fourier transform on R^n: Fourier transform on L^1, L^2 and the Schwartz space, interpolation of operators and the Fourier transform on L^p, sine and cosine transforms, Fourier transform of radially symmetric functions and Bessel transforms
  
• Fourier transform in the complex domain: Analyticity properties of Fourier transforms, Hardy spaces, Hilbert transform, Paley-Wiener theory
• Applications: may include selections from the following topics: sampling theory, differential equations, Sobolev spaces, Wiener-Hopf integral equations
  

Grading: The course grade will be based on 5-6 homework sets

Resources: There is no assigned textbook, but the following are very good references for some or all of the topics:

• Introduction to Fourier Analysis and Wavelets by M. Pinsky  
• Fourier Series and Integrals by H. Dym and H. McKean 
• Fourier Analysis by J. Duoandikoetxea 
• Introduction to Fourier Analysis on Euclidean Spaces by E. Stein and G. Weiss 
• Trigonometric Series by A. Zygmund 
• Fourier Analysis by T. Korner 
• An Introduction to Harmonic Analysis by Y. Katznelson
• Fourier Analysis: An Introduction by E. Stein and R. Shakarchi 
  

If a student has a disability that qualifies under the Americans with Disabilities Act and Section 504 of the Rehabilitation Act and requires accommodations, he/she should contact the Disability Resources (DR) office for information on appropriate policies and procedures. DR is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-6624.