Fourier–Bros–Iagolnitzer transform

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the FBI transform or Fourier–Bros–Iagolnitzer transform is a generalization of the <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a> developed by the French <a href="/facts/Mathematical_physics/sLKg8T1G">mathematical physicists</a> Jacques Bros and Daniel Iagolnitzer in order to characterise the <a href="/facts/Analytic_function/JhL3z8FP">local analyticity</a> of functions (or <a href="/facts/Distribution_(mathematics)/yfaJ4mUp">distributions</a>) on R<i>n</i>. The transform provides an alternative approach to analytic <a href="/facts/Wave_front_set/As2j99Tn">wave front sets</a> of distributions, developed  independently by the Japanese mathematicians <a href="/facts/Mikio_Sato/LUkFh98o">Mikio Sato</a>, <a href="/facts/Masaki_Kashiwara/29L71Lgt">Masaki Kashiwara</a> and Takahiro Kawai in their approach to <a href="/facts/Microlocal_analysis/rN65j9zV">microlocal analysis</a>. It can also be used to prove the analyticity of solutions of analytic <a href="/facts/Elliptic_partial_differential_equation/pQx2wB7V">elliptic partial differential equations</a> as well as a version of the classical uniqueness theorem, strengthening the <a href="/facts/Cauchy%E2%80%93Kowalevski_theorem/TBqUWjxU">Cauchy–Kowalevski theorem</a>, due to the Swedish mathematician <a href="/facts/Erik_Albert_Holmgren/TnaQhoUx">Erik Albert Holmgren</a> (1872–1943).
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Fourier–Bros–Iagolnitzer transform open-in-new

Fourier–Bros–Iagolnitzer transform