Math 658-600 Test 2 Review
Test 1 will be given on Wednesday, November 12, 2008. The test will be over sections 7.1-7.3, 7.5, 7.6 (DFT), 9.1, 9.4, and my notes on Discrete Fourier Transform. The test will consist of problems or propositions similar to homework problems or those done in class.
Fourier transforms and convolutions
- Convolutions and approximate identities
- Properties of the FT and finding FTs
- Convolution theorem, inversion theorem, Riemann-Lebesgue Lemma,
- L2 theory, Parseval's theorem
- Multivariate FT and radial functions
- DFT and FFT
- Applications
- Heat equation
- Sampling theorem
- Uncertainty principle
Tempered distributions
- Schwartz space, convergence in Schwartz space, FT of Schwartz functions
- Tempered distributions
- Derivatives
- Fourier transforms
- Multiplication by smooth functions
- Temperate convergence of distributions
- Periodic distributions, Poisson summation formula, applications
Updated 11/10/2008 (fjn).