Geodesic
The generating elements of certain Volterra operators connected with third- and fourth-order differential operators
Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 715-720

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Sufficient conditions are established for $f(x)$ to be the generating function for the Volterra operator which is inverse to the Cauchy operator: $l[y]=y^{(n)}+p_2(x)y^{(n-2)}+\dots+p_n(x)y$, $y(0)=y'(0)=\dots=y^{(n-1)}(0)=0$ ($n=3,4$), when the coefficients $p_i(x)$ are not analytic. 
@article{MZM_1968_3_6_a11,
     author = {A. P. Khromov},
     title = {The generating elements of certain {Volterra} operators connected with third- and fourth-order differential operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {715--720},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a11/}
}
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A. P. Khromov. The generating elements of certain Volterra operators connected with third- and fourth-order differential operators. Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 715-720. http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a11/