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
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 
@article{BASS_2001_26_a4,
     author = {A. Eida},
     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 },
     year = {2001},
     volume = {26},
     zbl = {1008.58018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2001_26_a4/}
}
TY  - JOUR
AU  - A. Eida
TI  - On the microlocal decomposition of ultradistributions and ultradifferentiable functions
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2001
SP  - 75 
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/BASS_2001_26_a4/
LA  - en
ID  - BASS_2001_26_a4
ER  - 
%0 Journal Article
%A A. Eida
%T On the microlocal decomposition of ultradistributions and ultradifferentiable functions
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2001
%P 75 
%V 26
%U http://geodesic.mathdoc.fr/item/BASS_2001_26_a4/
%G en
%F BASS_2001_26_a4
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/