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Tom Copeland
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What properties should a transform have to deserve the descriptor Fourier?

Two MO questions, "Heuristic behind the Fourier-Mukai transform" and "Explaining Mukai-Fourier transforms physically," compel me to ask these two related questions:

  1. What properties do you feel are essential for a transform to possess to be called a "Fourier" transform?

  2. What properties of the classical Fourier transform are not necessarily shared by a generalized "Fourier" transform?

In other words, how can I recognize a "Fourier" transform?

Tom Copeland
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