Harmonic Analysis

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  • Tell me about convergence of Fourier series. What can you say if you are given a continuous, periodic function? (Christ)
  • What is a Dirichlet kernel and what are its main properties? (Christ)
  • Tell me about the Poisson summation formula. What underlying ideas does it reflect? (Christ)
  • What form does a distribution supported at a point take? How do you know this? (Christ)
  • How do you solve Laplace's equation in a half space? In what sense do you have convergence to the boundary? What about L^\infty? What about pointwise convergence? (Christ)
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