Geodesic
The existence and uniqueness of a solution of Poisson's equation for generalized measures in an infinite-dimensional space
Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 825-834 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that a solution of Poisson's equation in the space of generalized measures on an infinite-dimensional, separable Hilbert space exists and is unique. Any generalized function concentrated at a point in an infinite-dimensional Hilbert space is equal to zero. 
@article{MZM_1976_20_6_a3,
     author = {V. Yu. Bentkus},
     title = {The existence and uniqueness of a~solution of {Poisson's} equation for generalized measures in an infinite-dimensional space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {825--834},
     year = {1976},
     volume = {20},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a3/}
}
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V. Yu. Bentkus. The existence and uniqueness of a solution of Poisson's equation for generalized measures in an infinite-dimensional space. Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 825-834. http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a3/