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Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\). (English. Russian original) Zbl 0236.47035

Funct. Anal. Appl. 5, 217-228 (1972); translation from Funkts. Anal. Prilozh. 5, No. 3, 54-69 (1971).

MSC:

47B50 Linear operators on spaces with an indefinite metric
47A10 Spectrum, resolvent
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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References:

[1] M. A. Naimark, ”Spectral functions of a symmetric operator,” Izv. Akad. Nauk SSSR, Ser. Matem.,4, 277-318 (1940). · JFM 66.0549.02
[2] M. A. Naimark, ”On spectral functions of a symmetric operator,” Izv. Akad. Nauk SSSR, Ser. Matem.,7, 285-296 (1943). · Zbl 0061.26005
[3] M. A. Naimark, ”On a representation of additive operators of functions of sets,” Dokl. Akad. Nauk SSSR,41, 373-375 (1943).
[4] M. G. Krein, ”On Hermitian operators with defect-indices equal to unity,” Dokl. Akad. Nauk SSSR,43, No. 8, 339-342 (1944).
[5] N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar, New York (1963). · Zbl 0098.30702
[6] M. G. Krein, ”On the resolvents of an Hermitian operator with defect-index (m, m),” Dokl. Akad. Nauk SSSR,52, No. 8, 657-660 (1946). · Zbl 0063.03358
[7] A. V. Shtraus, ”A generalization of the resolvent of symmetric operators,” Izv. Akad. Nauk SSSR, Ser. Matem.,18, 51-86 (1954).
[8] Sh. N. Saakyan, ”On the theory of the resolvents of a symmetric operator with infinite defect numbers,” Dokl. Akad. Nauk Armyansk. SSR,41, No. 4, 193-198 (1965). · Zbl 0163.37804
[9] M. G. Krein and Sh. N. Saakyan, ”On some new results in the theory of the resolvents of Hermitian operators,” Dokl. Akad. Nauk SSSR, 169, No. 6, 1269-1272 (1966).
[10] M. G. Krein and Sh. N. Saakyan, ”The resolvent matrix of an Hermitian operator and the characteristic functions associated with it,” Funktsional’. Analiz i Ego Prilozhen.,4, No. 3, 103-104 (1970).
[11] M. G. Krein and G. I. Langer, ”On a spectral function of a self-adjoint operator in a space with an indefinite metric,” Dokl. Akad. Nauk SSSR, 152, No. 1, 39-42 (1963).
[12] M. G. Krein and H. Langer, ”Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume ??,” Tikhvin Colloquium Memoirs: Operators and Operator Algebras of a Hilbert Space, [IX, 14-18 (1970)].
[13] A. V. Shtraus, ”Characteristic functions of linear operators,” Izv. Akad. Nauk SSSR, Ser. Matem.,24, 43-74 (1960).
[14] V. M. Adamyan, D. Arov, and M. G. Krein, ”Analytic properties of pairs of a Schmidt-Hankel operator and the generalized Sturm-Takagi problem,” Matem. Sb.,85 (1971).
[15] F. A. Berezin, ”On the model of Lie,” Matem. Sb.,60, 425-446 (1963).
[16] L. S. Pontryagin, ”Hermitian operators in a space with an indefinite metric,” Izv. Akad. Nauk SSSR, Ser. Matem.,8, 243-280 (1944). · Zbl 0061.26004
[17] I. Ts. Gokhberg and M. G. Krein, ”Fundamental data concerning defect numbers, root numbers, and indices of linear operators,” Uspekh. Matem. Nauk,12, No. 2, 43-118 (1957). · Zbl 0088.32101
[18] I. S. Iokhvidov and M. G. Krein, ”The spectral theory of linear operators in spaces with an indefinite metric, I, II,” Trudy Mosk. Matem. O-va,5, 367-432 (1956);8, 413-496 (1959). · Zbl 0072.13401
[19] Yu. L. Shmul’yan, ”On a class of holomorphic operator-functions,” Matem. Zametki,5, No. 3, 351-359 (1969).
[20] R. S. Phillips, ”Dissipative operators and hyperbolic systems of partial differential equations,” Trans. Amer. Math. Soc.,90, 192-254 (1959). · Zbl 0093.10001 · doi:10.1090/S0002-9947-1959-0104919-1
[21] B. Sz.-Nagy and A. Koranyi, ”Operatortheoretische Behandlung und Verallgemeinerung eines Problemkreises in der komplexen Funktionentheorie,” Acta Math., 100, 171-202 (1958). · Zbl 0083.34105 · doi:10.1007/BF02559538
[22] M. G. Krein, ”On J-extensional operators,” in Math. Studies, VI, Kishinev (1971).
[23] N. I. Akhiezer, The Classical Problem of Moments [in Russian], Fizmatgiz (1961). · Zbl 0124.06202
[24] G. Pick, ”Über die Beschränkungen analytischer Funktionen welche durch vorgegebene Funktionswete bewirkt sind,” Math. Ann.,77, 7-23 (1916). · JFM 45.0642.01 · doi:10.1007/BF01456817
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