Vitushkin, Anatoliy Georgievich

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Total publications: 53
Scientific articles: 39

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Member of the Russian Academy of Sciences
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.
List of publications on Google Scholar

Publications in Math-Net.Ru
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
17. A. Vitushkin, V. Telesnin, “Устойчивость усилителя и естественность звучания”, "Radio" Magazine, 1980, 7,  36–37  mathnet
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
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
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
21. A. G. Vitushkin, “On a problem of W. Rudin”, Dokl. Akad. Nauk SSSR, 213:1 (1973),  14–15  mathnet  mathscinet  zmath
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
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
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
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
27. A. G. Vitushkin, “Approximation of a function by rational fractions”, Dokl. Akad. Nauk SSSR, 171:5 (1966),  1023–1026  mathnet  mathscinet  zmath
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
29. A. G. Vitushkin, “Estimate of the Cauchy integral”, Mat. Sb. (N.S.), 71(113):4 (1966),  515–534  mathnet  mathscinet  zmath
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
31. A. G. Vitushkin, “Some properties of linear superpositions of smooth functions”, Dokl. Akad. Nauk SSSR, 156:5 (1964),  1003–1006  mathnet  mathscinet  zmath
32. A. G. Vitushkin, “On a problem of Denjoy”, Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964),  745–756  mathnet  mathscinet  zmath
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
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
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
36. A. G. Vitushkin, “The closest approximations of differentiable and analytic functions”, Dokl. Akad. Nauk SSSR, 119:3 (1958),  418–420  mathnet  mathscinet  zmath
37. A. G. Vitushkin, “The absolute $\varepsilon$-entropy of metric spaces”, Dokl. Akad. Nauk SSSR, 117:5 (1957),  745–747  mathnet  mathscinet  zmath
38. A. G. Vitushkin, “Some estimates from the tabulation theory”, Dokl. Akad. Nauk SSSR, 114:5 (1957),  923–926  mathnet  mathscinet  zmath
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
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

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
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
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
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
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
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
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
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
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
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
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), 191–192  isi
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
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

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