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Krein, Mark Grigor'evich
(1907–1989)

Statistics Math-Net.Ru
Total publications: 91
Scientific articles: 72

Number of views:
This page:4337
Abstract pages:36725
Full texts:17349
References:445

http://www.mathnet.ru/eng/person22217
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https://mathscinet.ams.org/mathscinet/MRAuthorID/189107

Publications in Math-Net.Ru
1981
1. M. G. Krein, G. K. Langer, “Continual analogues of orthogonal polynomials on the unit circle with respect to an indefinite weight, and the extension problems connected with them”, Dokl. Akad. Nauk SSSR, 258:3 (1981),  537–541  mathnet  mathscinet  zmath
2. D. Z. Arov, M. G. Krein, “Problem of search of the minimum of entropy in indeterminate extension problems”, Funktsional. Anal. i Prilozhen., 15:2 (1981),  61–64  mathnet  mathscinet  zmath; Funct. Anal. Appl., 15:2 (1981), 123–126  isi
1979
3. M. G. Krein, A. A. Nudelman, “On direct and inverse problems for the boundary dissipation frequencies of a nonuniform string”, Dokl. Akad. Nauk SSSR, 247:5 (1979),  1046–1049  mathnet  mathscinet  zmath
4. M. G. Krein, A. A. Nudelman, “Some propositions of the Fourier–Plancherel and Paley–Wiener type obtained by methods in the spectral theory of functions”, Funktsional. Anal. i Prilozhen., 13:4 (1979),  79–80  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:4 (1979), 301–303
1978
5. M. G. Krein, I. E. Ovcharenko, “Inverse problems for Q-functions and resolvent matrices of positive hermitian operators”, Dokl. Akad. Nauk SSSR, 242:3 (1978),  521–524  mathnet  mathscinet  zmath
6. M. G. Krein, “Measurable Hermitian-positive functions”, Mat. Zametki, 23:1 (1978),  79–91  mathnet  mathscinet  zmath; Math. Notes, 23:1 (1978), 45–50
7. V. M. Adamyan, D. Z. Arov, M. G. Krein, “7.6. The approximation by functions in $H^\infty+C$”, Zap. Nauchn. Sem. LOMI, 81 (1978),  190–192  mathnet; J. Soviet Math., 26:5 (1984), 2224–2225
1977
8. M. G. Krein, I. M. Spitkovsky, “On factorization of matrix-valued functions on the unit circle”, Dokl. Akad. Nauk SSSR, 234:2 (1977),  287–290  mathnet  mathscinet  zmath
1976
9. M. G. Krein, I. E. Ovcharenko, “On generalized resolvents and resolvent matrices of positive Hermitian operators”, Dokl. Akad. Nauk SSSR, 231:5 (1976),  1063–1066  mathnet  mathscinet  zmath
10. M. G. Krein, G. K. Langer, “On the indefinite power moment problem”, Dokl. Akad. Nauk SSSR, 226:2 (1976),  261–264  mathnet  mathscinet  zmath
1975
11. M. G. Krein, P. Ya. Nudel'man, “Approximation of $L_2(\omega_1,\omega_2)$ Functions by Minimum-Energy Transfer Functions of Linear Systems”, Probl. Peredachi Inf., 11:2 (1975),  37–60  mathnet  mathscinet  zmath; Problems Inform. Transmission, 11:2 (1975), 124–142
1973
12. M. G. Krein, P. Ya. Nudel'man, “On some new problems for Hardy class functions and continuous families of functions with double orthogonality”, Dokl. Akad. Nauk SSSR, 209:3 (1973),  537–540  mathnet  mathscinet  zmath
13. M. G. Krein, “A hypothesis of A. M. Lyapunov”, Funktsional. Anal. i Prilozhen., 7:3 (1973),  45–54  mathnet  mathscinet  zmath; Funct. Anal. Appl., 7:3 (1973), 204–212
1971
14. M. G. Krein, G. K. Langer, “Defective subspaces and generalized resolvents of an Hermitian operator in the space $\Pi_\varkappa$”, Funktsional. Anal. i Prilozhen., 5:3 (1971),  54–69  mathnet  mathscinet  zmath; Funct. Anal. Appl., 5:3 (1971), 217–228
15. M. G. Krein, G. K. Langer, “Defect subspaces and generalized resolvents of an Hermitian operator in the space $\Pi_\varkappa$”, Funktsional. Anal. i Prilozhen., 5:2 (1971),  59–71  mathnet  mathscinet  zmath; Funct. Anal. Appl., 5:2 (1971), 136–146
16. V. M. Adamyan, D. Z. Arov, M. G. Krein, “Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur–Takagi problem”, Mat. Sb. (N.S.), 86(128):1(9) (1971),  34–75  mathnet  mathscinet  zmath; Math. USSR-Sb., 15:1 (1971), 31–73
1970
17. M. G. Krein, F. É. Melik-Adamyan, “Some applications of the theorem on factorization of a unitary matrix”, Funktsional. Anal. i Prilozhen., 4:4 (1970),  73–75  mathnet  mathscinet  zmath; Funct. Anal. Appl., 4:4 (1970), 327–329
18. M. G. Krein, Sh. N. Saakyan, “Resolvent matrix of Hermitian operator and the characteristic functions related to it”, Funktsional. Anal. i Prilozhen., 4:3 (1970),  103–104  mathnet  mathscinet  zmath; Funct. Anal. Appl., 4:3 (1970), 258–259
19. V. M. Brodskii, I. Ts. Gokhberg, M. G. Krein, “Determination and fundamental properties of the characteristic function of $\mathcal{Y}$-node”, Funktsional. Anal. i Prilozhen., 4:1 (1970),  88–90  mathnet  mathscinet  zmath; Funct. Anal. Appl., 4:1 (1970), 78–80
1969
20. V. M. Brodskii, I. Ts. Gokhberg, M. G. Krein, “General theorems on triangular representations of linear operators and multiplications of their characteristic functions”, Funktsional. Anal. i Prilozhen., 3:4 (1969),  1–27  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:4 (1969), 255–276
21. V. M. Adamyan, D. Z. Arov, M. G. Krein, “Bounded operators that commute with a contraction of class $C_{00}$ of unit rank of nonunitarity”, Funktsional. Anal. i Prilozhen., 3:3 (1969),  86–87  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:3 (1969), 242–243
22. M. G. Krein, “Angular localization of the spectrum of a multiplicative integral in a Hilbert space”, Funktsional. Anal. i Prilozhen., 3:1 (1969),  89–90  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:1 (1969), 73–74
1968
23. V. M. Adamyan, D. Z. Arov, M. G. Krein, “Infinite Hankel matrices and generalized Caretheodory–Fejer and I. Schur Problems”, Funktsional. Anal. i Prilozhen., 2:4 (1968),  1–17  mathnet  mathscinet  zmath; Funct. Anal. Appl., 2:4 (1968), 269–281
24. V. M. Adamyan, D. Z. Arov, M. G. Krein, “Infinite hankel matrices and generalized Carathéodory–Fejer and Riesz problems”, Funktsional. Anal. i Prilozhen., 2:1 (1968),  1–19  mathnet  mathscinet  zmath; Funct. Anal. Appl., 2:1 (1968), 1–18
1967
25. I. Ts. Gokhberg, M. G. Krein, “Triangular representations of linear operators and multiplicative representations of their characteristic functions”, Dokl. Akad. Nauk SSSR, 175:2 (1967),  272–275  mathnet  mathscinet  zmath
26. I. Ts. Gokhberg, M. G. Krein, “Description of contraction operators which are similar to unitary operators”, Funktsional. Anal. i Prilozhen., 1:1 (1967),  38–60  mathnet  mathscinet  zmath; Funct. Anal. Appl., 1:1 (1967), 33–52
1966
27. M. G. Krein, Yu. L. Shmul'yan, “A class of operators in a space with an indefinite metric”, Dokl. Akad. Nauk SSSR, 170:1 (1966),  34–37  mathnet  mathscinet  zmath
28. M. G. Krein, Sh. N. Saakyan, “Certain new results in the theory of resolvents of Hermitian operators”, Dokl. Akad. Nauk SSSR, 169:6 (1966),  1269–1272  mathnet  mathscinet  zmath
1965
29. I. Ts. Gokhberg, M. G. Krein, “Multiplicative representation of the characteristic functions of operators close to unitary”, Dokl. Akad. Nauk SSSR, 164:4 (1965),  732–735  mathnet  mathscinet  zmath
1964
30. M. G. Krein, G. K. Langer, “On the theory of quadratic pencils of self-adjoint operators”, Dokl. Akad. Nauk SSSR, 154:6 (1964),  1258–1261  mathnet  mathscinet  zmath
31. M. G. Krein, “A new application of the fixed-point principle in the theory of operators in a space with indefinite metric”, Dokl. Akad. Nauk SSSR, 154:5 (1964),  1023–1026  mathnet  mathscinet  zmath
1963
32. M. G. Krein, G. K. Langer, “On the spectral function of a self-adjoint operator in a space with indefinite metric”, Dokl. Akad. Nauk SSSR, 152:1 (1963),  39–42  mathnet  mathscinet  zmath
1962
33. I. Ts. Gokhberg, M. G. Krein, “On the problem of factoring operators in a Hilbert space”, Dokl. Akad. Nauk SSSR, 147:2 (1962),  279–282  mathnet  mathscinet  zmath
34. M. Sh. Birman, M. G. Krein, “On the theory of wave operators and scattering operators”, Dokl. Akad. Nauk SSSR, 144:3 (1962),  475–478  mathnet  mathscinet  zmath
35. M. G. Krein, “On perturbation determinants and a trace formula for unitary and self-adjoint operators”, Dokl. Akad. Nauk SSSR, 144:2 (1962),  268–271  mathnet  mathscinet  zmath
36. M. G. Krein, G. Ya. Lyubarskii, “Analytic properties of the multipliers of periodic canonical differential systems of positive type”, Izv. Akad. Nauk SSSR Ser. Mat., 26:4 (1962),  549–572  mathnet  mathscinet  zmath
1961
37. I. Ts. Gokhberg, M. G. Krein, “Volterra operators with imaginary component in one class or another”, Dokl. Akad. Nauk SSSR, 139:4 (1961),  779–782  mathnet  mathscinet  zmath
38. I. Ts. Gokhberg, M. G. Krein, “On the theory of triangular representations of nonselfadjoint operators”, Dokl. Akad. Nauk SSSR, 137:5 (1961),  1034–1037  mathnet  mathscinet  zmath
1960
39. M. G. Krein, “A contribution to the theory of linear non-selfadjoined operators”, Dokl. Akad. Nauk SSSR, 130:2 (1960),  254–256  mathnet  mathscinet  zmath
1959
40. I. S. Iokhvidov, M. G. Krein, “Spectral theory of operators in spaces with indefinite metric. II”, Tr. Mosk. Mat. Obs., 8 (1959),  413–496  mathnet  mathscinet  zmath
41. M. G. Krein, “Criteria for completeness of a system of root vectors of a dissipative operator”, Uspekhi Mat. Nauk, 14:3(87) (1959),  145–152  mathnet  mathscinet  zmath
1958
42. I. Ts. Gokhberg, M. G. Krein, “On the stable system of partial indices in the Hilbert problem for many unknown functions”, Dokl. Akad. Nauk SSSR, 119:5 (1958),  854–857  mathnet  mathscinet  zmath
43. I. S. Kats, M. G. Krein, “Criteria for the discreteness of the spectrum of a singular string”, Izv. Vyssh. Uchebn. Zaved. Mat., 1958, 2,  136–153  mathnet  mathscinet
44. M. G. Krein, “Integral equations on the half-line with a kernel depending on the difference of the arguments”, Uspekhi Mat. Nauk, 13:5(83) (1958),  3–120  mathnet  mathscinet  zmath
45. I. Ts. Gokhberg, M. G. Krein, “Systems of integral equations on the half-line with kernels depending on the difference of the arguments”, Uspekhi Mat. Nauk, 13:2(80) (1958),  3–72  mathnet  mathscinet  zmath
1957
46. M. G. Krein, “On a continuous analogue of a Christoffel formula from the theory of orthogonal polynomials”, Dokl. Akad. Nauk SSSR, 113:5 (1957),  970–973  mathnet  mathscinet  zmath
47. M. G. Krein, “On Bari bases of a Hilbert space”, Uspekhi Mat. Nauk, 12:3(75) (1957),  333–341  mathnet  mathscinet  zmath
48. I. Ts. Gokhberg, M. G. Krein, “Fundamental aspects of defect numbers, root numbers and indexes of linear operators”, Uspekhi Mat. Nauk, 12:2(74) (1957),  43–118  mathnet  mathscinet  zmath
1956
49. I. S. Iokhvidov, M. G. Krein, “Spectral theory of operators in space with indefinite metric. I”, Tr. Mosk. Mat. Obs., 5 (1956),  367–432  mathnet  mathscinet  zmath
1955
50. M. G. Krein, P. G. Rekhtman, “Development in a new direction of the Chebyshev–Markov theory of limiting values of integrals”, Uspekhi Mat. Nauk, 10:1(63) (1955),  67–78  mathnet  mathscinet  zmath
1953
51. M. G. Krein, “On the trace formula in perturbation theory”, Mat. Sb. (N.S.), 33(75):3 (1953),  597–626  mathnet  mathscinet  zmath
1952
52. M. G. Krein, “On the indeterminate case of the Sturm–Liouville boundary problem in the interval $(0,\infty)$”, Izv. Akad. Nauk SSSR Ser. Mat., 16:4 (1952),  293–324  mathnet  mathscinet  zmath
53. M. G. Krein, M. A. Krasnosel'skii, “Stability of the index of an unbounded operator”, Mat. Sb. (N.S.), 30(72):1 (1952),  219–224  mathnet  mathscinet  zmath
1951
54. M. G. Krein, “The ideas of P. L. Chebyshev and A. A. Markov in the theory of limiting values of integrals and their further development”, Uspekhi Mat. Nauk, 6:4(44) (1951),  3–120  mathnet  mathscinet  zmath
55. M. G. Krein, “On the application of an algebraic proposition in the theory of matrices of monodromy”, Uspekhi Mat. Nauk, 6:1(41) (1951),  171–177  mathnet  mathscinet  zmath
1950
56. M. G. Krein, “On an application of the fixed point principle in the theory of linear transformations of spaces with an indefinite metric”, Uspekhi Mat. Nauk, 5:2(36) (1950),  180–190  mathnet  mathscinet  zmath
57. S. I. Zukhovitskii, M. G. Krein, “Remark on a possible generalization of the theorems of A. Haar and A. N. Kolmogorov”, Uspekhi Mat. Nauk, 5:1(35) (1950),  217–229  mathnet  mathscinet  zmath
1948
58. M. G. Krein, “On some questions related to the ideas of Lyapunov in the theory of stability”, Uspekhi Mat. Nauk, 3:3(25) (1948),  166–169  mathnet  mathscinet
1947
59. M. Krein, “A contribution to the theory of entire functions of exponential type”, Izv. Akad. Nauk SSSR Ser. Mat., 11:4 (1947),  309–326  mathnet  mathscinet  zmath
60. M. G. Krein, M. A. Krasnosel'skii, “Fundamental theorems on the extension of Hermitian operators and certain of their applications to the theory of orthogonal polynomials and the problem of moments”, Uspekhi Mat. Nauk, 2:3(19) (1947),  60–106  mathnet  mathscinet
61. M. G. Krein, “The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. II”, Rec. Math. [Mat. Sbornik] N.S., 21(63):3 (1947),  365–404  mathnet  mathscinet  zmath
62. M. Krein, “The theory of self-adjoint extensions of somi-bcunded Hermitian transformations and its applications. I”, Rec. Math. [Mat. Sbornik] N.S., 20(62):3 (1947),  431–495  mathnet  mathscinet  zmath
1946
63. M. Krein, “Sur un théorème de M. Vygodsky”, Rec. Math. [Mat. Sbornik] N.S., 18(60):3 (1946),  447–450  mathnet  mathscinet  zmath
1943
64. Mark Krein, Selim Krein, “Sur l'espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semiordonnés”, Rec. Math. [Mat. Sbornik] N.S., 13(55):1 (1943),  1–38  mathnet  mathscinet  zmath
1937
65. M. Krein, “Sur les opérateurs différentials autoadjoints et leurs fonctions de Green symétriques”, Rec. Math. [Mat. Sbornik] N.S., 2(44):6 (1937),  1023–1072  mathnet  zmath
66. M. Krein, “Sur les développements des fonctions arbitraires en séries de fonctions fondamentales d'un problème aux limits quelconque”, Rec. Math. [Mat. Sbornik] N.S., 2(44):5 (1937),  923–933  mathnet  zmath
67. M. Krein, “Sur les valeurs caractéristiques des noyaux symétriques dérivables”, Rec. Math. [Mat. Sbornik] N.S., 2(44):4 (1937),  725–732  mathnet  zmath
1935
68. F. Gantmakher, M. Krein, “Sur une classe spéciale de déterminants ayant le rapport aux noyaux de Kellog”, Mat. Sb., 42:4 (1935),  501–508  mathnet  zmath
1934
69. Mark Krein, “Über die Knoten der harmonischen Schwingungen einiger spezieller mechanischer Systeme”, Mat. Sb., 41:2 (1934),  339–348  mathnet  zmath
1933
70. M. Krein, “Über eine neue Klasse von Hermiteschen Formen und über eine Verallgemeinerung des trigonometrischen Momentenproblems”, Bulletin de l'Académie des Sciences de l'URSS. Classe des sciences mathématiques et na, 1933, 9,  1259–1275  mathnet  zmath
71. M. Krein, “Über das Spektrum der Jakobischen Form in Verbindung mit der Theorie der Torsionsschwingungen von Walzen”, Mat. Sb., 40:4 (1933),  455–466  mathnet  zmath
72. M. Krein, “Zur Theorie der symmetrischen Polynome”, Mat. Sb., 40:3 (1933),  271–283  mathnet  zmath

1987
73. Yu. M. Berezanskii, I. M. Gel'fand, M. G. Krein, S. G. Krein, Yu. A. Mitropol'skii, A. V. Skorokhod, “Yurii L'vovich Daletskii (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 42:4(256) (1987),  213–214  mathnet  mathscinet; Russian Math. Surveys, 42:4 (1987), 183–185  isi
74. I. M. Gel'fand, M. G. Krein, V. A. Marchenko, N. K. Nikol'skii, I. V. Ostrovskii, “Boris Yakovlevich Levin (on his eightieth birthday)”, Uspekhi Mat. Nauk, 42:4(256) (1987),  207–210  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:4 (1987), 175–176  isi
1985
75. Yu. M. Berezanskii, M. G. Krein, S. L. Sobolev, E. M. Semenov, “Iosif Semenovich Iokhvidov (obituary)”, Uspekhi Mat. Nauk, 40:6(246) (1985),  131–132  mathnet  mathscinet; Russian Math. Surveys, 40:6 (1985), 113–115  isi
76. M. G. Gasymov, M. G. Krein, B. Ya. Levin, V. A. Marchenko, I. S. Sargsyan, S. L. Sobolev, “Boris Moiseevich Levitan (on his seventieth birthday)”, Uspekhi Mat. Nauk, 40:2(242) (1985),  209–210  mathnet  mathscinet; Russian Math. Surveys, 40:2 (1985), 247–249  isi
1981
77. N. N. Bogolyubov, I. M. Gel'fand, R. L. Dobrushin, A. A. Kirillov, M. G. Krein, D. A. Leites, R. A. Minlos, Ya. G. Sinai, M. A. Shubin, “Feliks Aleksandrovich Berezin (obituary)”, Uspekhi Mat. Nauk, 36:4(220) (1981),  185–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 36:4 (1981), 209–216  isi
78. A. N. Kolmogorov, M. G. Krein, B. Ya. Levin, B. M. Levitan, Yu. I. Lyubich, V. A. Marchenko, I. V. Ostrovskii, A. Ya. Povzner, A. V. Pogorelov, “Naum Il'ich Akhiezer (obituary)”, Uspekhi Mat. Nauk, 36:4(220) (1981),  183–184  mathnet  mathscinet  zmath; Russian Math. Surveys, 36:4 (1981), 207–208  isi
1980
79. I. M. Gel'fand, M. I. Graev, D. P. Zhelobenko, R. S. Ismagilov, M. G. Krein, L. D. Kudryavtsev, S. M. Nikol'skii, A. Ya. Helemskii, A. V. Strauss, “Mark Aronovich Naimark (obituary)”, Uspekhi Mat. Nauk, 35:4(214) (1980),  135–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:4 (1980), 157–164  isi
1977
80. N. I. Akhiezer, N. V. Efimov, M. G. Krein, M. A. Lavrent'ev, V. A. Marchenko, I. V. Ostrovskii, B. V. Shabat, “Boris Yakovlevich Levin (on his seventieth birthday)”, Uspekhi Mat. Nauk, 32:5(197) (1977),  211–213  mathnet  mathscinet  zmath; Russian Math. Surveys, 32:5 (1977), 181–184
1971
81. Yu. M. Berezanskii, A. N. Kolmogorov, M. G. Krein, B. Ya. Levin, B. M. Levitan, V. A. Marchenko, “Naum Il'ich Akhiezer (on his seventieth birthday)”, Uspekhi Mat. Nauk, 26:6(162) (1971),  257–261  mathnet  mathscinet  zmath; Russian Math. Surveys, 26:6 (1971), 233–237
1968
82. N. V. Efimov, M. G. Krein, I. V. Ostrovskii, “Boris Yakovlevich Levin (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 23:5(143) (1968),  187–191  mathnet  mathscinet  zmath; Russian Math. Surveys, 23:5 (1968), 141–145
1967
83. M. G. Krein, “First Voronezh Winter Mathematical School”, Uspekhi Mat. Nauk, 22:4(136) (1967),  189–190  mathnet
1966
84. I. S. Iokhvidov, M. G. Kreĭn, “Letter to the editor”, Tr. Mosk. Mat. Obs., 15 (1966),  452–454  mathnet  mathscinet  zmath
1965
85. M. A. Aizerman, M. G. Krein, L. A. Lyusternik, M. A. Naimark, L. S. Pontryagin, S. L. Sobolev, S. A. Khristianovich, Ya. B. Shor, “Feliks Ruvimovich Gantmakher (obituary)”, Uspekhi Mat. Nauk, 20:2(122) (1965),  149–157  mathnet  mathscinet  zmath; Russian Math. Surveys, 20:2 (1965), 143–151
86. M. G. Krein, “Vitol'd L'vovich Shmul'yan (on the fiftieth anniversary of his birth and the twentieth anniversary of his death)”, Uspekhi Mat. Nauk, 20:2(122) (1965),  131–133  mathnet  mathscinet  zmath; Russian Math. Surveys, 20:2 (1965), 127–129
1961
87. M. G. Krein, B. Ya. Levin, “Naum Il'ich Akhiezer (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 16:4(100) (1961),  223–234  mathnet  mathscinet  zmath; Russian Math. Surveys, 16:4 (1961), 129–141
1960
88. M. G. Krein, G. E. Shilov, “Mark Aronovich Naimark (on the occasion of his fiftieth birthday)”, Uspekhi Mat. Nauk, 15:2(92) (1960),  231–236  mathnet  mathscinet  zmath; Russian Math. Surveys, 15:2 (1960), 169–174
1958
89. I. Ts. Gokhberg, M. G. Krein, “Errata”, Uspekhi Mat. Nauk, 13:4(82) (1958),  232  mathnet
1957
90. I. S. Iokhvidov, M. G. Krein, “Remark to the article “Spectral theory of operators in space with indefinite metric. I” (Trudy Mosk. Mat. O-va 5 (1956))”, Tr. Mosk. Mat. Obs., 6 (1957),  486  mathnet
1948
91. M. G. Krein, M. A. Rutman, “Linear operators leaving invariant a cone in a Banach space”, Uspekhi Mat. Nauk, 3:1(23) (1948),  3–95  mathnet  mathscinet  zmath

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