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Vitushkin, Anatoliy Georgievich
(1931–2004)
Statistics Math-Net.Ru
Total publications: 54
Scientific articles: 40

Number of views:
This page:4458
Abstract pages:27717
Full texts:13327
References:1429
Member of the Russian Academy of Sciences
Professor
Doctor of physico-mathematical sciences (1958)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 25.06.1931
Keywords: funcion theory and related topics of applied mathematics; complex analysis and algebraic geometry; information theory and radio engineering.
   
Main publications:
  • Vitushkin A. G. Coding of signals with finite spektrum and sound recording problem. Proc. of the Intern. Congr. of Math., Vancouver, 1974.

https://www.mathnet.ru/eng/person11659
https://ru.wikipedia.org/wiki/Vitushkin_Anatolii_Georgievich
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:vitushkin.a-g
https://mathscinet.ams.org/mathscinet/MRAuthorID/190683
https://elibrary.ru/author_items.asp?authorid=4651

Publications in Math-Net.Ru Citations
2004
1. A. G. Vitushkin, “On Hilbert's thirteenth problem and related questions”, Uspekhi Mat. Nauk, 59:1(355) (2004),  11–24  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:1 (2004), 11–25  isi  scopus 34
1999
2. A. G. Vitushkin, “Evaluation of the Jacobian of a rational transformation of $\mathbb C^2$ and some applications”, Mat. Zametki, 66:2 (1999),  308–312  mathnet  mathscinet  zmath; Math. Notes, 66:2 (1999), 245–249  isi 10
3. A. G. Vitushkin, “A criterion for the representability of a chain of $\sigma$-processes by a composition of triangular chains”, Mat. Zametki, 65:5 (1999),  643–653  mathnet  mathscinet  zmath; Math. Notes, 65:5 (1999), 539–547  isi 10
1998
4. A. G. Vitushkin, “On the homology of a ramified covering over $\mathbb C^2$”, Mat. Zametki, 64:6 (1998),  839–846  mathnet  mathscinet  zmath  elib; Math. Notes, 64:6 (1998), 726–731  isi 11
1987
5. A. G. Vitushkin, “Uniform approximation of functions by holomorphic functions”, Trudy Mat. Inst. Steklov., 176 (1987),  300–307  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 176 (1988), 301–308 1
1985
6. A. G. Vitushkin, “Holomorphic mappings and the geometry of surfaces”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 7 (1985),  167–226  mathnet  mathscinet  zmath 9
7. A. G. Vitushkin, “Remarkable facts about complex analysis”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 7 (1985),  5–22  mathnet  mathscinet  zmath 1
8. A. G. Vitushkin, “Extension of the germ of a holomorphic map of a strictly pseudo-convex surface”, Uspekhi Mat. Nauk, 40:4(244) (1985),  151–152  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:4 (1985), 229–230  isi 1
9. A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Uspekhi Mat. Nauk, 40:2(242) (1985),  3–31  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:2 (1985), 1–35  isi 21
10. A. G. Vitushkin, V. V. Ezhov, N. G. Kruzhilin, “Continuation of holomorphic mappings along real-analytic hypersurfaces”, Trudy Mat. Inst. Steklov., 167 (1985),  60–95  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 167 (1986), 63–102 4
1984
11. A. G. Vitushkin, “Analysis of power series specifying automorphisms of a hypersurface in connection with the problem of extension of a mapping”, Trudy Mat. Inst. Steklov., 163 (1984),  37–41  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 163 (1985), 47–51 1
1983
12. A. G. Vitushkin, V. V. Ezhov, N. G. Kruzhilin, “Extension of local mappings of pseudoconvex surfaces”, Dokl. Akad. Nauk SSSR, 270:2 (1983),  271–274  mathnet  mathscinet  zmath; Dokl. Math., 27 (1983), 580–583  isi 10
13. A. G. Vitushkin, “Global normalization of a real-analytic surface along a chain”, Dokl. Akad. Nauk SSSR, 269:1 (1983),  15–18  mathnet  mathscinet  zmath 5
1982
14. A. G. Vitushkin, S. M. Ivashkovich, “On the extension of holomorphic mappings of a real analytic hypersurface into complex projective space”, Dokl. Akad. Nauk SSSR, 267:4 (1982),  779–780  mathnet  mathscinet  zmath 2
15. A. G. Vitushkin, “Holomorphic extension of mappings of compact hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982),  28–35  mathnet  mathscinet  zmath; Math. USSR-Izv., 20:1 (1983), 27–33 11
1981
16. V. K. Beloshapka, A. G. Vitushkin, “Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981),  962–984  mathnet  mathscinet  zmath; Math. USSR-Izv., 19:2 (1982), 241–259 14
1980
17. A. Vitushkin, V. Telesnin, “Устойчивость усилителя и естественность звучания”, "Radio" Magazine, 1980, no. 7,  36–37  mathnet
1978
18. A. G. Vitushkin, M. S. Mel'nikov, “3.7. Analytic capacity and rational approximation”, Zap. Nauchn. Sem. LOMI, 81 (1978),  207–209  mathnet; J. Soviet Math., 26:5 (1984), 2237–2238
1975
19. A. G. Vitushkin, “Uniform approximations by holomorphic functions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 4 (1975),  5–12  mathnet  mathscinet  zmath; J. Soviet Math., 5:5 (1976), 607–611 10
1974
20. V. I. Buslaev, A. G. Vitushkin, “An estimate of the code length of signals with a finite spectrum in connection with sound-recording problems”, Izv. Akad. Nauk SSSR Ser. Mat., 38:4 (1974),  867–895  mathnet  mathscinet  zmath; Math. USSR-Izv., 8:4 (1974), 867–894 6
1973
21. A. G. Vitushkin, “On a problem of W. Rudin”, Dokl. Akad. Nauk SSSR, 213:1 (1973),  14–15  mathnet  mathscinet  zmath 4
1971
22. A. G. Vitushkin, “Certain examples in connection with problems about polynomial transformations of $C^n$”, Izv. Akad. Nauk SSSR Ser. Mat., 35:2 (1971),  269–279  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:2 (1971), 278–288 13
1967
23. A. G. Vitushkin, “Analytic capacity and the Cauchy integral”, Dokl. Akad. Nauk SSSR, 175:1 (1967),  20–23  mathnet  mathscinet  zmath
24. A. G. Vitushkin, “The analytic capacity of sets in problems of approximation theory”, Uspekhi Mat. Nauk, 22:6(138) (1967),  141–199  mathnet  mathscinet  zmath; Russian Math. Surveys, 22:6 (1967), 139–200 134
25. A. G. Vitushkin, G. M. Henkin, “Linear superpositions of functions”, Uspekhi Mat. Nauk, 22:1(133) (1967),  77–124  mathnet  mathscinet  zmath; Russian Math. Surveys, 22:1 (1967), 77–125 33
1966
26. A. G. Vitushkin, “Conditions on a set which are necessary and sufficient in order that any continuous function, analytic at its interior points, admit uniform approximation by rational fractions”, Dokl. Akad. Nauk SSSR, 171:6 (1966),  1255–1258  mathnet  mathscinet  zmath 3
27. A. G. Vitushkin, “Approximation of a function by rational fractions”, Dokl. Akad. Nauk SSSR, 171:5 (1966),  1023–1026  mathnet  mathscinet  zmath 2
28. A. G. Vitushkin, “A proof of upper semicontinuity of a set variation”, Dokl. Akad. Nauk SSSR, 166:5 (1966),  1022–1025  mathnet  mathscinet  zmath 3
29. A. G. Vitushkin, “Estimate of the Cauchy integral”, Mat. Sb. (N.S.), 71(113):4 (1966),  515–534  mathnet  mathscinet  zmath 3
1964
30. A. G. Vitushkin, “A proof of the existence of analytic functions of several variables not representable by linear superpositions of continuously differentiable functions of fewer variables”, Dokl. Akad. Nauk SSSR, 156:6 (1964),  1258–1261  mathnet  mathscinet  zmath 5
31. A. G. Vitushkin, “Some properties of linear superpositions of smooth functions”, Dokl. Akad. Nauk SSSR, 156:5 (1964),  1003–1006  mathnet  mathscinet  zmath 4
32. A. G. Vitushkin, “On a problem of Denjoy”, Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964),  745–756  mathnet  mathscinet  zmath 3
1963
33. A. G. Vitushkin, L. D. Ivanov, M. S. Mel'nikov, “Incommensurability of the minimal linear measure with the length of a set”, Dokl. Akad. Nauk SSSR, 151:6 (1963),  1256–1259  mathnet  mathscinet  zmath 1
1958
34. A. G. Vitushkin, “Some theorems on the possibility of a uniform approximation of continuous functions by analytic functions”, Dokl. Akad. Nauk SSSR, 123:6 (1958),  959–962  mathnet  mathscinet  zmath 2
35. A. G. Vitushkin, “Analytic capacity of sets and some of its properties”, Dokl. Akad. Nauk SSSR, 123:5 (1958),  778–781  mathnet  mathscinet  zmath 2
36. A. G. Vitushkin, “The closest approximations of differentiable and analytic functions”, Dokl. Akad. Nauk SSSR, 119:3 (1958),  418–420  mathnet  mathscinet  zmath 4
1957
37. A. G. Vitushkin, “The absolute $\varepsilon$-entropy of metric spaces”, Dokl. Akad. Nauk SSSR, 117:5 (1957),  745–747  mathnet  mathscinet  zmath 2
38. A. G. Vitushkin, “Some estimates from the tabulation theory”, Dokl. Akad. Nauk SSSR, 114:5 (1957),  923–926  mathnet  mathscinet  zmath 4
39. A. G. Vitushkin, “The relation of variation of a set to the metric properties of its complement”, Dokl. Akad. Nauk SSSR, 114:4 (1957),  686–689  mathnet  mathscinet  zmath 1
1954
40. A. G. Vitushkin, “Sufficient conditions for the boundedness of the linear variation of a function of three variables”, Mat. Sb. (N.S.), 34(76):2 (1954),  307–322  mathnet  mathscinet  zmath 1
2004
41. A. G. Vitushkin, A. A. Gonchar, M. V. Samokhin, V. M. Tikhomirov, P. L. Ul'yanov, V. P. Havin, V. Ya. Èiderman, “Semën Yakovlevich Khavinson (obituary)”, Uspekhi Mat. Nauk, 59:4(358) (2004),  186–192  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:4 (2004), 777–785  isi 1
2002
42. A. G. Vitushkin, “Half a century as one day”, Uspekhi Mat. Nauk, 57:1(343) (2002),  191–206  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:1 (2002), 199–220  isi 2
43. A. A. Bolibrukh, A. G. Vitushkin, V. S. Vladimirov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul'yanov, L. D. Faddeev, E. M. Chirka, “Andrei Aleksandrovich Gonchar (on his 70th birthday)”, Uspekhi Mat. Nauk, 57:1(343) (2002),  185–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:1 (2002), 191–198  isi 5
1997
44. A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, V. V. Napalkov, S. M. Nikol'skii, A. M. Sedletskii, P. L. Ul'yanov, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (1917–1987) (on the 80th anniversary of his birth)”, Uspekhi Mat. Nauk, 52:3(315) (1997),  189–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:3 (1997), 635–637  isi 3
45. A. G. Vitushkin, A. A. Gonchar, M. V. Samokhin, P. L. Ul'yanov, “Semen Yakovlevich Khavinson (on his 70th birthday)”, Uspekhi Mat. Nauk, 52:3(315) (1997),  187–188  mathnet  mathscinet; Russian Math. Surveys, 52:3 (1997), 631–633  isi 1
1996
46. O. V. Besov, V. M. Buchstaber, A. G. Vitushkin, A. A. Gonchar, S. V. Konyagin, L. D. Kudryavtsev, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, A. Yu. Popov, V. A. Sadovnichii, A. F. Sidorov, Yu. N. Subbotin, S. A. Telyakovskii, P. L. Ul'yanov, N. I. Chernykh, “Sergei Borisovich Stechkin (obituary)”, Uspekhi Mat. Nauk, 51:6(312) (1996),  3–10  mathnet  mathscinet; Russian Math. Surveys, 51:6 (1996), 1007–1014  isi 4
1995
47. A. G. Vitushkin, A. A. Gonchar, S. M. Nikol'skii, E. A. Sevast'yanov, S. B. Stechkin, P. L. Ul'yanov, “Evgenii Prokof'evich Dolzhenko (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 50:1(301) (1995),  217–218  mathnet  mathscinet; Russian Math. Surveys, 50:1 (1995), 227–229  isi 2
1990
48. V. I. Arnol'd, A. G. Vitushkin, E. A. Gorin, V. Ya. Lin, Yu. V. Nesterenko, V. M. Tikhomirov, P. L. Ul'yanov, A. B. Shidlovskii, M. A. Shubin, “Vyacheslav Alekseevich Oleinikov (obituary)”, Uspekhi Mat. Nauk, 45:1(271) (1990),  163–165  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:1 (1990), 191–194  isi 2
1987
49. A. G. Vitushkin, A. A. Gonchar, E. P. Dolzhenko, V. V. Napalkov, A. M. Sedletskii, S. B. Stechkin, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev”, Mat. Zametki, 42:4 (1987),  483–493  mathnet  mathscinet; Math. Notes, 42:4 (1987), 765–772  isi
50. A. G. Vitushkin, A. A. Gonchar, B. S. Kashin, A. I. Kostrikin, S. M. Nikol'skii, S. P. Novikov, P. L. Ul'yanov, L. D. Faddeev, “Evgenii Mikhailovich Nikishin (obituary)”, Uspekhi Mat. Nauk, 42:5(257) (1987),  183–188  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:5 (1987), 153–160  isi 5
51. A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, V. V. Napalkov, S. M. Nikol'skii, A. M. Sedletskii, P. L. Ul'yanov, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (obituary)”, Uspekhi Mat. Nauk, 42:5(257) (1987),  177–182  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:5 (1987), 145–152  isi 3
52. A. G. Vitushkin, A. A. Gonchar, V. A. Zorich, P. L. Ul'yanov, “Boris Vladimirovich Shabat (on his seventieth birthday)”, Uspekhi Mat. Nauk, 42:4(256) (1987),  217–218  mathnet  mathscinet; Russian Math. Surveys, 42:4 (1987), 191–193  isi 1
1986
53. A. G. Vitushkin, M. I. Zelikin, N. N. Krasovskii, S. P. Novikov, Yu. S. Osipov, K. A. Sitnikov, “Nicolai Terent'evich Tynyanskii (obituary)”, Uspekhi Mat. Nauk, 41:4(250) (1986),  143–144  mathnet  mathscinet; Russian Math. Surveys, 41:4 (1986), 173–174  isi 1
1979
54. N. U. Arakelian, A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, “Mkhitar Mkrtichevich Dzhrbashyan (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 34:2(206) (1979),  235–240  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:2 (1979), 269–275 1

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