Geodesic
Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem
Sbornik. Mathematics, Tome 18 (1972) no. 3, pp. 425-471 
Z. I. Leibenzon. Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. Sbornik. Mathematics, Tome 18 (1972) no. 3, pp. 425-471. http://geodesic.mathdoc.fr/item/SM_1972_18_3_a4/
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     title = {Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Results obtained by the author in RZhMat., 1972, 6B684 are generalized to the case of a countable set of indices $\mathfrak N$. This allows the author to find necessary and sufficient conditions for the existence of a system of boundary-value problems with simple spectrum, having a given set of eigenvalues and weight numbers. Bibliography: 10 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

[3] Z. L. Leibenzon, “Spektralnye razlozheniya otobrazhenii sistem kraevykh zadach”, Trudy Mosk. matem. ob-va, XXV (1971), 15–58 | MR

[4] Z. L. Leibenzon, “Algebraiko-differentsialnye preobrazovaniya lineinykh differentsialnykh operatorov lyubogo poryadka i ikh spektralnye svoistva, primenimye v obratnoi zadache. I. Sluchai konechnogo $\mathfrak{R}$”, Matem. sbornik, 87(129) (1971), 396–416 | MR

[5] Helge von Koch, “Sur quelques points de la theorie des determinanfes infinies”, Acta Math., 24 (1900), 89–122 | MR

[6] Helge von Koch, “Sur la convergence des determinantes infinies”, Rend. Palermo,, 28 (1909), 255–266 | DOI

[7] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Fizmatgiz, Moskva, 1965

[8] Z. L. Leibenzon, “O lineinykh otobrazheniyakh, soderzhaschikh kompleksnyi parametr”, Teoriya funkts., funkts. analiz i ikh prilozh., no. 5, Kharkov, 1967, 189–200 | MR | Zbl

[9] M. A. Naimark, Lineinye differentsialnye operatory, Gostekhizdat, Moskva, 1954

[10] N. Danford, Dzh. T. Shvarts, Lineinye operatory. Obschaya teoriya, IL, Moskva, 1962