On generalized resolvents of Hermitian relations in Krein spaces

Journal of Mathematical Sciences

Volumn 97, Issue 5, 1999, Pages 4420-4460

  Derkach, V A ^a  

^a NONE

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EID: 0012973345     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02366102     Document Type: Article

References (58)

1. T. I. Azizov, "On the theory of extensions of J-isometric and J-symmetric operators," Funkt. Anal. Pril., 18, No. 1, 57-58 (1984).
2. T. I. Azizov and I. S. Iochvidov, Foundations of the Theory of Linear Operators in Spaces with Indenfinite Metric [in Russian], Nauka, Moscow (1986).
3. D. Z. Arov, "Passive linear stationary dynamical systems," Sib. Mat. Zh., 20, No. 2 (144), 211-228 (1979).
4. N. I. Akhiezer, Classical Moment Problem, [in Russian], Fizmatgiz, Moscow (1961).
5. V. M. Bruk, "On invertible restrictions of closed operators in Banach spaces", in: Fund. Anal. Spectral Theory [in Russian], Gos. Ped. Inst., Ul'yanovsk, 32-42 (1988).
6. A. N. Vernik and M. S. Chunaeva, "Characteristic function of a linear relation in a space with indefinite metric," in: Funct. Anal. Spectral Theory [in Russian], Gos. Ped. Inst., Ul'yanovsk, 42-52 (1981).
7. M. I. Višik, "On general boundary value problems for elliptic differential equations," Tr. Mosk. Mat. Obshchestva, 1, 187-246 (1952).
8. V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
9. V. A. Derkach, "Extensions of an Hermitian operator in a Krein space," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 5-9 (1988).
10. V. A. Derkach, "On extensions of a nondensely denned Hermitian operator in a Krein space," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 15-19 (1990).
11. V. A. Derkach and M. M. Malamud, "On the Weyl function and Hermitian operators with gaps," Dokl. Akad. Nauk SSSR, 293, No. 5, 1041-1046 (1987).
12. V. A. Derkach and M. M. Malamud, "Generalized resolvents of Hermitian operators and the truncated moment problem," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 34-39 (1991).
13. V. A. Derkach and M. M. Malamud, "Inverse problems for Weyl functions, preresolvent and resolvent matrices of Hermitian operators," Dokl. Akad. Nauk SSSR, 326, No. 1, 12-18 (1992).
14. T. Kato, Perturbation Theory for Linear Operators, Springer, Heidelberg (1966).
15. A. N. Kochubei, "On characteristic functions of symmetric operators and their extensions," Izv. Akad. Nauk Arm. SSR, Mat., No. 5, 218-232 (1980).
16. M. G. Krein, "On an Hermitian operator with deficiency indices equal to one," Dokl. Akad. Nauk SSSR, 43, No. 8, 339-342 (1944).
17. M. G. Krein, "On resolvents of an Hermitian operator with defect indices (m,m)," Dokl. Akad. Nauk SSSR, 52, No. 8, 657-660 (1946).
18. M. G. Krein, "Foundations of the representation theory of an Hermitian operator with deficiency indices {m,m)," Ukr. Math. Zh., 1, 3-66 (1949).
19. M. G. Krein, "The description of solutions of the truncated moment problem," Math. Issledov., Kishinev, 2, No. 2, 114-132 (1967).
20. κ," Part 1: Funkts. Anal. Prilozhen., 5, No. 2, 59-71 (1971);
21. Part 2: Funkts. Anal. Prilozhen., 5, No. 3, 54-69 (1971).
22. M. G. Krein and H. Langer, "On the indefinite moment problem," Dokl. Akad. Nauk SSSR, 226, No. 2, 261-264 (1976).
23. M. G. Krein and A. A. Nudel'man, The Markov Moment Problem and Extremal Problems [in Russian], Nauka, Moscow (1973).
24. M. G. Krein and Sh. N. Saakyan, "On some new results in the theory of resolvents of Hermitian operators," Dokl. Akad. Nauk SSSR, 169, No. 6, 1269-1272 (1966).
25. M. G. Krein and Sh. N. Saakyan, "Resolvent matrix of an Hermitian operator and the related characteristic functions," Funkts. Anal. Prilozhen., 4, No. 3, 103-104 (1970).
26. A. V. Kuzhel, "Regular extensions of Hermitian operators in a space with an indefinite metric," Dokl. Akad. Nauk SSSR, 265, No. 5, 199-201 (1982).
27. M. M. Malamud, "On a formula of generalized resolvents of a nondensely denned Hermitian operator," Ukr. Mat. Zh., 44, No. 12, 1658-1683 (1992).
28. A. A. Nikonov, "On generalized resolvents of a densely defined operator in a space with an indefinite metric," in: Funkts. Anal., Gos. Ped. Inst., Ul'yanovsk, No. 2, 42-45, (1974).
29. F. S. Rofe-Beketov, "On self-adjoint extensions of differential operators in a space of vector-valued functions," Teor. Funkts, Funkts. Anal. Prilozhen., 8, 3-24 (1969).
30. Sh. N. Saakyan, "On the theory of resolvents of a symmetric operator with infinite deficiency indices," Dokl. Akad. Nauk Arm. SSR, 41, No. 4, 193-198 (1965).
31. Yu. L. Shmul'yan, "Regular and singular Hermitian operators," Mat. Zametki, 8, No. 2, 197-203 (1970).
32. 3 and related models," Teor. Mat. Fiz., 65, No. 1, 24-34 (1985).
33. A. V. Shtraus, "Characteristic functions of linear operators," Izv. Akad. Nauk SSSR, Ser. Mat., 24, No. 1, 43-74 (1960).
34. A. V. Shtraus, "On self-adjoint operators in the orthogonal sum of Hilbert spaces," Dokl. Akad. Nauk SSSR, 144, No. 5, 512-515 (1962).
35. A.V. Shtraus, "Extensions and generalized resolvents of a nondensely defined symmetric operator," Izv. Akad. Nauk SSSR, Ser. Mat, 34, No. 1, 175-202 (1970).
36. E. A. Coddington, "Extension theory of formally normal and symmetric subspaces," Mem. Amer. Math. Soc, No. 134, 1-80 (1973).
37. C. Benewitz, "Symmetric relations on a Hilbert space," Led. Notes Math., 280, 212-218 (1972).
38. J. Bognar, Indefinite Inner Product Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
39. κ," Math. Nachr., 120, 275-294 (1985).
40. C. Davis, "J-unitary dilation of a general operator," Acta Sci. Math. Szeged, 31, 74-86 (1970).
41. V. Derkach, "On the Weyl function and generalized resolvents of an Hermitian operator in a Krein space," Integr. Equat. Oper. Theory, 23, 387-415 (1995).
42. V. Derkach, "On the indefinite moment problem and resolvent matricies of Hermitian operators in Krein spaces," Math. Nachr., 184, 1-32 (1997).
43. V. A. Derkach and M. M. Malamud, "Generalized resolvents and the boundary value problems for Hermitian operators with gaps," J. Funct. Anal., 95, No. 1, 1-95 (1991).
44. V. Derkach and M. M. Malamud, "The extension theory of Hermitian operators and the moment problem," J. Math. Sci., 73, No. 2, 141-242 (1995).
45. A. Dijksma, H. Langer, and H. S. V. de Snoo, "Unitary colligations in Krein spaces and their role in the extension theory," Lect. Notes Math., 1242, 1-42, (1987).
46. A. Dijksma, H. Langer, and H. S. V. de Snoo, "Generalized coresolvents of standard isometric relations in Krein spaces," in: Operator Theory: Adv. and Appl., 48, 261-274 (1990).
47. A. Dijksma and H. S. V. de Snoo, "Selfadjoint extensions of symmetric subspaces," Pacif. J. Math., 54, No. 1, 71-100 (1974).
48. A. Dijksma and H. S. V. de Snoo, "Symmetric and self-adjoint relations in Krein spaces," Part 1: Operator Theory: Adv. and Appl., 24, 145-166 (1987);
49. Part 2: Ann. Acad. Sci. Fenn. Ser. A, Math., 12, 199-216 (1987).
50. I. S. Iochvidov, M. G. Krein, and H. Langer, "Introduction to the spectral theory of operators in Krein spaces with an indefinite metric," Math. Res., Berlin, 9 (1982).
51. κ," Acta. Sci. Math. Szeged, 34, 191-230 (1973).
52. κ zusammenhangen. I. Einige Funktionenklassen und ihre Darstellungen," Math. Nachr., 77, 187-236 (1977).
53. κ. 3. Indefinite analogs of the Hamburger and Stieltjes moment problems," Part 1: Beitrage Anal., 14, 25-40 (1979);
54. Part 2: Beitrage Anal., 15, 27-45 (1981).
55. H. Langer, "Spectral functions of definable operators in Krein spaces," Functional Analysis (Dubrovhik 1981),
56. Lect. Notes Math., 948, 1-46 (1982).
57. H. Langer and B. Textorius, "On generalized resolvents and Q-functions of symmetric linear relations in Hilbert spaces," Pacif. J. Math., 72, No. 1, 135-165 (1977).
58. H. Langer and B. Textorius, "L-resolvent matrices of symmetric linear relations with equal defect numbers," Integr. Equat. Oper. Theory, 5, 208-243 (1982).