Geodesic
On the microlocal decomposition of ultradistributions and ultradifferentiable functions
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 75 .

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The microlocal decomposition for ultradistributions and ultradifferentiable functions is derived by Bengel-Schapira's method and these classes of functions are microlocalized as subsheaves $\FC_M^*$, $\FC_M^{d,*}$ of the sheaf $\FC_M$ of Sato's microfunctions on a real analytic manifold $M$. Moreover, the exactness of the sequences $\sexact{\FA_M}{\FDB^*_M}{\pi_*\FC^*_M}$ and $\sexact{\FA_M}{\FDF^*_M}{\pi_*\FC_M^{d,*}}$ is shown and some fundamental properties on $\FC_M^*$, $\FC_M^{d,*}$ are described. Here $\FDB^*_M$ is a sheaf of ultradistributions and $\FDF^*_M$ is a sheaf of ultradifferentiable functions. We give some solvability conditions applicable to partial differential equations by operating Aoki's classes of microdifferential operators of infinite order on these sheaves.
Classification : 58J15
Keywords: hyperfunctions, ultradistributions, ultradifferentiable functions, microdifferential operators 
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     title = {On the microlocal decomposition of ultradistributions and ultradifferentiable functions},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {75 },
     publisher = {mathdoc},
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     year = {2001},
     zbl = {1008.58018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2001_26_a4/}
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A. Eida. On the microlocal decomposition of ultradistributions and ultradifferentiable functions. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 75 . http://geodesic.mathdoc.fr/item/BASS_2001_26_a4/