Harmonic Analysis on Finite Abelian Groups

  title={Harmonic Analysis on Finite Abelian Groups},
  author={Paul Koester},
We give a discussion of harmonic analysis on finite abelian groups, emphasizing various ways in which the structure of the group is encoded on various spaces of functions, ways in which the Fourier transform detects and preserves these structures. We discuss the major tools, like convolutions and Fourier transforms, along with some fundamental theorems, like the Plancheral, Parseval, Fourier inversion, and Poisson summation formulas, and fundamental heuristic principles, like the uncertainty… CONTINUE READING

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