The FBI transform of f is defined for a ≥ 0 by
Thus, when a = 0, it essentially coincides with the Fourier transform.
The same formulas can be used to define the Fourier and FBI transforms of tempered distributions in S'(Rn).
Read more about FBI Transform: Inversion Formula, Criterion For Local Analyticity, Holmgren's Uniqueness Theorem, The Analytic Wave Front Set
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