Geodesic
Eigenfunctions and associated functions of an $n$-th-order linear differential operator
Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 869-878 
M. S. Eremin. Eigenfunctions and associated functions of an $n$-th-order linear differential operator. Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 869-878. http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a8/
@article{MZM_1976_20_6_a8,
     author = {M. S. Eremin},
     title = {Eigenfunctions and associated functions of an $n$-th-order linear differential operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {869--878},
     year = {1976},
     volume = {20},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For $n\ge2$ we consider a differential operator $$ L[y]\equiv z^ny^{(n)}+P_1(z)z^{n-1}y{(n-1)}+_2(z)z^{n-2}Y^{(n-2)}+\dots+P_n(z)y=\mu y;\quad P_1,\dots,P_n(z)\in A_R $$ here $A_R$ is the space of functions which are analytic in the disk $|z|, equipped with the topology of compact convergence. We prove the existence of sequences $\{f_k(z)\}_{k=0}^\infty$, consisting of a finite number of associated functions of the operator $L$ and an infinite number of its eigenfunctions; we show that the sequence forms a basis in $A_r$ for an arbitrary $\{f_k(z)\}_{k=0}^\infty$; and we establish some additional properties of the sequencephiv $\{f_k(z)\}_{k=0}^\infty$