Geodesic
The problem of representing an arbitrary linear operator in the form of a differential operator of infinite order
Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 277-283 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider linear operators, acting continuously from the space $A_{R_1}$ of functions analytic in the disk $|z| into the space $A_{R_2}$. We show that every such operator may be represented in the form of a linear differential operator of infinite order with coefficients analytic in the disk $|z|. 
@article{MZM_1974_16_2_a11,
     author = {Yu. F. Korobeinik},
     title = {The problem of representing an arbitrary linear operator in the form of a~differential operator of infinite order},
     journal = {Matemati\v{c}eskie zametki},
     pages = {277--283},
     year = {1974},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a11/}
}
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Yu. F. Korobeinik. The problem of representing an arbitrary linear operator in the form of a differential operator of infinite order. Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 277-283. http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a11/