Geodesic
Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 408-428 
Z. I. Leibenzon. Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$. Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 408-428. http://geodesic.mathdoc.fr/item/SM_1972_16_3_a6/
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Linear differential operators $R$ of order $n$ from $C^n[0,1]$ into $C[0,1]$, i.e. without boundary conditions, are discussed. With $\lambda$ complex, let $Z^R_\lambda$ denote the linear space of all solutions $z(x)\in C^n[0,1]$ of the homogeneous equation $Rz=\lambda z$. We use die operator $R$ and certain of its spectral properties to obtain an operator $L$ analogous to $R$. Our main result is to obtain expressions defining a linear mapping $T_\lambda\colon Z_\lambda^R\to Z_\lambda^L$ (Theorem 2.6). The linear mappings $T_\lambda$ are meromorphically dependent on $\lambda$. Bibliography: 2 titles.

[1] Z. L. Leibenzon, “Obratnaya zadacha spektralnogo analiza obyknovennykh differentsialnykh operatorov vysshikh poryadkov”, Trudy Mosk. matem. ob-va, XV (1966), 70–144 | MR

[2] Z. L. Leibenzon, “Edinstvennost resheniya obratnoi zadachi dlya obyknovennykh differentsialnykh operatorov poryadka $n\geqslant2$ i preobrazovaniya takikh operatorov”, DAN SSSR, 142:3 (1962), 534–537 | MR | Zbl