Geodesic
Representation of Hermitian operators with improper scale subspace
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 554-564 Cet article a éte moissonné depuis la source Math-Net.Ru

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The theory of representation of Hermitian operators, constructed by M. G. Krein (UMZh, 1, 2, 1949, 3–66), is carried over to the case where the scale subspace may contain improper elements. Defect numbers of the operator are possibly infinite, and its domain may fail to be dense. Bibliography: 11 titles. 
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Yu. L. Shmul'yan. Representation of Hermitian operators with improper scale subspace. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 554-564. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a5/

[1] M. G. Krein, “Osnovnye polozheniya teorii predstavleniya ermitovykh operatorov s indeksom defekta $(m,m)$”, Ukr. matem. zh., 1:2 (1949), 3–66 | MR | Zbl

[2] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[3] M. G. Krein, Analiticheskie problemy i rezultaty v teorii lineinykh operatorov v gilbertovom prostranstve (Moskva, 1966), Trudy Mezhdunarodnogo kongressa matematikov, Mir, Moskva, 1968

[4] Yu. L. Shmulyan, “Zobrazheniya ermitovogo operatora z uzagalnenim modulem”, DAN URSR, seriya A, 5 (1970), 432–436

[5] Yu. L. Shmulyan, “Rasshirennye rezolventy i rasshirennye spektralnye funktsii ermitova operatora”, Matem. sb., 84(126) (1971), 440–455 | Zbl

[6] I. Ts. Gokhberg, A. S. Markus, “Dve teoremy o rastvore podprostranstv banakhova prostranstva”, Uspekhi matem. nauk, XIV:5(89) (1969), 97–112

[7] I. Ts. Gokhberg, A. S. Markus, “Kharakteristicheskie svoistva nekotorykh tochek spektra lineinykh ogranichennykh operatorov”, Izv. VUZov, Matematika, 1960, no. 2(15), 74–87 | MR | Zbl

[8] I. S. Kats, M. G. Krein, “$R$-funktsii – analiticheskie funktsii, otobrazhayuschie verkhnyuyu poluploskost v sebya”, Dopolnenie I k kn.: F. Atkinson, Diskretnye i nepreryvnye kraevye zadachi, Mir, Moskva, 1968 | MR

[9] Yu. L. Daletskii, S. G. Krein, “Formuly differentsirovaniya po parametru funktsii ermitovykh operatorov”, DAN SSSR, 76:1 (1951), 13–16

[10] H. Langer, “Über die Methode der richtenden Fiumktiomale von M. G. Krein”, Acta Math. Hungarica, 21 (1970), 207–224 | DOI | MR | Zbl

[11] M. S. Livshits, Kand. dissertatsiya, Maikop, 1942