Geodesic
Generalized functions which are analytic with respect to some of their variables
Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 333-341 
Yu. A. Brychkov. Generalized functions which are analytic with respect to some of their variables. Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 333-341. http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a2/
@article{MZM_1975_18_3_a2,
     author = {Yu. A. Brychkov},
     title = {Generalized functions which are analytic with respect to some of their variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {333--341},
     year = {1975},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a generalized function which is analytic with respect to some of its variables in the sense of Gording and Malgrange we prove a theorem on representation in the form of a power series in these variables which converges in $D'$ and a corresponding uniqueness theorem. We also obtain necessary and sufficient conditions for a generalized function to be entire with respect to some of its variables.