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 Dirichlet conditions - Definition 

In mathematics, the Dirichlet conditions are the conditions that must be met for a function, f(x), to have a Fourier transform. Dirichlet conditions are named after Johann Peter Gustav Lejeune Dirichlet.

The conditions are:

  • f(x) must be single-valued
  • f(x) must have a finite number of extrema in any given interval
  • f(x) must have a finite number of discontinuities in any given interval
  • f(x) must be absolutely integrable

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