The discussion centers on the implications of removing the infinity assumption in the Fourier Transform (FT) and its effect on the uncertainty principle. It is established that the infinity assumption refers to the requirement for functions to fall away quickly enough at infinity for the FT to exist. The distribution approach to Fourier Transforms does not necessitate this condition, and the uncertainty principle remains valid within Schwartz Space, as outlined in the referenced papers. Bill confirms that the uncertainty principle applies to all functions within this mathematical framework.
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