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Havinson, Semen Yakovlevich
(1927–2003)
Statistics Math-Net.Ru
Total publications: 54
Scientific articles: 52

Number of views:
This page:3376
Abstract pages:14557
Full texts:6574
References:572
Professor
Doctor of physico-mathematical sciences (1962)
Birth date: 17.05.1927
Keywords: analytic functions; potential; capacities; extremal problems; approximation.

Subject:

The general approach to solving extremal problems in various classis of analytic functions, based on duality relations between extremums, was developed. This method was developed also to the investigation extremal problems with supplementary conditions. The general theory such processes of the approximation, when the magnitude of the approximating aggregates take into account, was developed in Banach spaces. Faktorization theory for analytic functions on compact Riemann surfaces with boundary was constructed. The extremal problem analytic capacity in arbitrary domains was investigated and a theory of the extremal problems like the analytic capacity for Golubev sums was constructed. The Chebyshev theorem for the best approximation of a function of two variables by means of sum functions of one variable was proved.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1949 (department of theory of functions). Ph.D. thesis was defended in 1953. D.Sci. thesis was defended in 1962. Professor — 1963. Honorary professor — 1996. A list of my works contains more than 180 titles.
   
Main publications:
  • Khavinson S. Ya. Extremal problems in complex analysis // AMS Translations. Series 2, v. 129, 1986, 1–114.
  • Khavinson S. Ya. Best Approximation by Linear Superpositions (Approximate Nomography) // AMS Translations of Mathem. Monographs. V. 159, 1997, 1–175.

https://www.mathnet.ru/eng/person9063
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/195926

Publications in Math-Net.Ru Citations
2003
1. S. Ya. Khavinson, “Duality relations in the theory of analytic capacity”, Algebra i Analiz, 15:1 (2003),  3–62  mathnet  mathscinet  zmath; St. Petersburg Math. J., 15:1 (2004), 1–40 4
2002
2. S. Ya. Havinson, “Approximations by wedge elements taking into account the values of the approximating elements”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 10,  71–84  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 46:10 (2002), 69–82 1
1999
3. S. Ya. Havinson, “Extremal problems for Golubev sums”, Mat. Zametki, 65:5 (1999),  738–745  mathnet  mathscinet  zmath; Math. Notes, 65:5 (1999), 620–626  isi
4. S. Ya. Havinson, “Golubev sums: a theory of extremal problems like the analytic capacity problem and of related approximation processes”, Uspekhi Mat. Nauk, 54:4(328) (1999),  75–142  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:4 (1999), 753–818  isi  scopus 6
1996
5. A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “Existence of the best possible uniform approximation of a function of several variables by a sum of functions of fewer variables”, Mat. Sb., 187:5 (1996),  3–14  mathnet  mathscinet  zmath; Sb. Math., 187:5 (1996), 623–634  isi  scopus 3
1995
6. S. Ya. Havinson, “The annihilator of linear superpositions”, Algebra i Analiz, 7:3 (1995),  1–42  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:3 (1996), 307–341 1
7. S. Ya. Khavinson, “Some approximation properties of linear superpositions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 8,  63–73  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 60–70 1
8. A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “On existence of a best uniform approximation of a function in two variables by the sums $\varphi(x)+\psi(y)$”, Sibirsk. Mat. Zh., 36:4 (1995),  819–827  mathnet  mathscinet  zmath; Siberian Math. J., 36:4 (1995), 707–713  isi 8
1994
9. S. Ya. Havinson, “On interpolation properties of exterior functions in Kolmogorov superpositions”, Mat. Zametki, 55:4 (1994),  104–113  mathnet  mathscinet  zmath; Math. Notes, 55:4 (1994), 406–412  isi 3
1990
10. S. Ya. Khavinson, “A method for removing the multivalence of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 11,  64–72  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:11 (1990), 80–90 1
1989
11. S. Ya. Havinson, “Factorization theory for single-valued analytic functions on compact Riemann surfaces with boundary”, Uspekhi Mat. Nauk, 44:4(268) (1989),  155–189  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:4 (1989), 113–156  isi 6
12. S. Ya. Khavinson, “Factorization of single-valued analytic functions of compact bordered Riemann surfaces”, Zap. Nauchn. Sem. LOMI, 170 (1989),  285–313  mathnet  mathscinet  zmath; J. Soviet Math., 63:2 (1993), 275–290 2
1985
13. S. Ya. Havinson, “Representation of functions of two variables by the sums $\phi(x)+\psi(y)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 2,  66–73  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 29:2 (1985), 81–90 4
1981
14. S. Ya. Havinson, “On a class of sharp estimates for polynomials, moments, and analytic functions”, Uspekhi Mat. Nauk, 36:5(221) (1981),  199–200  mathnet  mathscinet  zmath; Russian Math. Surveys, 36:5 (1981), 157–158  isi
15. S. Ya. Havinson, “On a class of sharp inequalities for polynomials, moments and analytic functions”, Sibirsk. Mat. Zh., 22:6 (1981),  188–207  mathnet  mathscinet  zmath; Siberian Math. J., 22:6 (1981), 949–964  isi 1
1978
16. S. Ya. Khavinson, “19.5. The exact majorant problem”, Zap. Nauchn. Sem. LOMI, 81 (1978),  167–168  mathnet; J. Soviet Math., 26:5 (1984), 2207
1977
17. O. A. Muradyan, S. Ya. Khavinson, “Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem”, Mat. Zametki, 22:2 (1977),  269–276  mathnet  mathscinet  zmath; Math. Notes, 22:2 (1977), 641–645 6
1974
18. S. Ya. Khavinson, “On the distribution of zeroes of extremal functions in $E_p$-classes in finitely connected domains”, Mat. Zametki, 16:6 (1974),  879–885  mathnet  mathscinet  zmath; Math. Notes, 16:6 (1974), 1122–1125
19. S. Ya. Khavinson, “Representation of extremal functions in the classes $E_q$ in terms of Green's and Neumann's functions”, Mat. Zametki, 16:5 (1974),  707–716  mathnet  mathscinet  zmath; Math. Notes, 16:5 (1974), 1018–1023 3
1972
20. S. Ya. Havinson, Z. S. Romanova, “Approximation properties of finite-dimensional subspaces in $L_1$”, Mat. Sb. (N.S.), 89(131):1(9) (1972),  3–15  mathnet  mathscinet  zmath; Math. USSR-Sb., 18:1 (1972), 1–14 2
1971
21. S. Ya. Havinson, “Some approximation theorems involving the magnitude of the coefficients of the approximating functions”, Dokl. Akad. Nauk SSSR, 196:6 (1971),  1283–1286  mathnet  mathscinet  zmath 4
1969
22. S. Ya. Havinson, “A Chebyshev theorem for the approximation of a function of two variables by sums of the type $\varphi(x)+\psi(y)$”, Izv. Akad. Nauk SSSR Ser. Mat., 33:3 (1969),  650–666  mathnet  mathscinet  zmath; Math. USSR-Izv., 3:3 (1969), 617–632 15
23. S. Ya. Khavinson, “Permissible values of coefficients of polynomials in uniform approximation of continuous functions”, Mat. Zametki, 6:5 (1969),  619–625  mathnet  mathscinet  zmath; Math. Notes, 6:5 (1969), 834–838 7
1967
24. S. Ya. Havinson, “Approximation by elements of convex sets”, Dokl. Akad. Nauk SSSR, 172:2 (1967),  294–297  mathnet  mathscinet  zmath 3
25. S. Ya. Havinson, “Boundary values of arbitrary functions”, Russian Math. Surveys, 22:1 (1967), 127–131  mathnet
1965
26. S. Ya. Havinson, “On the Rudin–Carleson theorem”, Dokl. Akad. Nauk SSSR, 165:3 (1965),  497–499  mathnet  mathscinet  zmath
27. S. Ya. Havinson, “Analytic functions of bounded type”, Itogi Nauki. Mat. Anal. 1963, 1965,  5–80  mathnet  mathscinet  zmath 7
1963
28. S. Ya. Havinson, “Åxtremal problems for bounded analytic functions with interior side conditions”, Uspekhi Mat. Nauk, 18:2(110) (1963),  25–98  mathnet  mathscinet  zmath; Russian Math. Surveys, 18:2 (1963), 23–96 18
1961
29. V. P. Havin, S. Ya. Havinson, “Some estimates of analytic capacity”, Dokl. Akad. Nauk SSSR, 138:4 (1961),  789–792  mathnet  mathscinet  zmath 3
30. S. Ya. Havinson, “Some problems concerning the completeness of systems”, Dokl. Akad. Nauk SSSR, 137:4 (1961),  793–796  mathnet  mathscinet  zmath 6
31. S. Ya. Khavinson, “On two classes of extremal problems for polynomials and moments”, Izv. Akad. Nauk SSSR Ser. Mat., 25:4 (1961),  557–590  mathnet  mathscinet  zmath 3
32. S. Ya. Khavinson, “The analytic capacity of sets related to the non-triviality of various classes of analytic functions, and on Schwarz's lemma in arbitrary domains”, Mat. Sb. (N.S.), 54(96):1 (1961),  3–50  mathnet  mathscinet  zmath 9
33. S. Ya. Khavinson, “On approximation with account taken of the size of the coefficients of the approximants”, Trudy Mat. Inst. Steklov., 60 (1961),  304–324  mathnet  mathscinet  zmath 4
1960
34. S. Ya. Havinson, “Extremum problems for functions satisfying some supplementary restrictions inside the region and the application of these problems to questions of approximation”, Dokl. Akad. Nauk SSSR, 135:2 (1960),  270–273  mathnet  mathscinet  zmath 2
35. S. Ya. Havinson, “Approximation on sets of zero analytic capacity”, Dokl. Akad. Nauk SSSR, 131:1 (1960),  44–46  mathnet  mathscinet  zmath 3
36. S. Ya. Havinson, “On a class of extremal problems for polynomials”, Dokl. Akad. Nauk SSSR, 130:5 (1960),  997–1000  mathnet  mathscinet 2
37. S. Ya. Havinson, “On the radius of holomorphy of functions inverse to functions which are analytic and bounded in multiply-connected regions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1960, no. 5,  190–194  mathnet  mathscinet  zmath
38. Yu. E. Alenitsyn, S. Ya. Khavinson, “The radius of $p$-valence for bounded analytic functions in multiply-connected domains”, Mat. Sb. (N.S.), 52(94):1 (1960),  653–657  mathnet  mathscinet  zmath 1
1959
39. G. Ts. Tumarkin, S. Ya. Havinson, “Mutual orthogonality of boundary values of certain classes of analytic functions in multiply connected domains”, Uspekhi Mat. Nauk, 14:3(87) (1959),  173–180  mathnet  mathscinet  zmath 2
1958
40. G. Ts. Tumarkin, S. Ya. Khavinson, “Properties of extremum functions in extremum problems for certain classes of analytic functions with a weighed metric”, Dokl. Akad. Nauk SSSR, 119:2 (1958),  215–218  mathnet  mathscinet  zmath
41. G. Ts. Tumarkin, S. Ya. Havinson, “Existence in multiply-connected regions of single-valued analytic functions with a given modulus of boundary values”, Izv. Akad. Nauk SSSR Ser. Mat., 22:4 (1958),  543–562  mathnet  mathscinet  zmath 5
42. G. Ts. Tumarkin, S. Ya. Havinson, “Analytic functions on multiply-connected regions of the class of V. I. Smirnov (class $S$)”, Izv. Akad. Nauk SSSR Ser. Mat., 22:3 (1958),  379–386  mathnet  mathscinet  zmath 2
43. S. Ya. Havinson, “On uniqueness of functions of best approximation in the metric of the space $L_1$”, Izv. Akad. Nauk SSSR Ser. Mat., 22:2 (1958),  243–270  mathnet  mathscinet  zmath 2
44. S. Ya. Havinson, “The radii of univalence, starlikeness and convexity of a class of analytic functions in multiply-connected domains”, Izv. Vyssh. Uchebn. Zaved. Mat., 1958, no. 3,  233–240  mathnet  mathscinet  zmath 1
45. G. Ts. Tumarkin, S. Ya. Havinson, “An expansion theorem for analytic functions of class $E_p$ in multiply connected domains”, Uspekhi Mat. Nauk, 13:2(80) (1958),  223–228  mathnet  mathscinet  zmath 1
46. G. Ts. Tumarkin, S. Ya. Havinson, “Classes of analytic functions in multiply connected regions represented by Cauchy–Green formulas”, Uspekhi Mat. Nauk, 13:2(80) (1958),  215–221  mathnet  mathscinet  zmath 3
47. G. Ts. Tumarkin, S. Ya. Havinson, “On the definition of analytic functions of class $E_p$ in multiply connected domains”, Uspekhi Mat. Nauk, 13:1(79) (1958),  201–206  mathnet  mathscinet  zmath 8
48. G. Ts. Tumarkin, S. Ya. Havinson, “Investigation of the properties of extremal functions by means of duality relations in extremal problems for classes of analytic functions in multiply connected domains”, Mat. Sb. (N.S.), 46(88):2 (1958),  195–228  mathnet  mathscinet  zmath 6
49. G. Ts. Tumarkin, S. Ya. Havinson, “Conditions for the representability of a harmonic function by Green's formula in a multiply-connected region”, Mat. Sb. (N.S.), 44(86):2 (1958),  225–234  mathnet  mathscinet  zmath 1
1957
50. G. Ts. Tumarkin, S. Ya. Havinson, “On the removing of singularities for analytic functions of a certain class (class $D$)”, Uspekhi Mat. Nauk, 12:4(76) (1957),  193–199  mathnet  mathscinet  zmath 1
1955
51. S. Ya. Havinson, “Extremal problems for certain classes of analytic functions in finitely connected regions”, Mat. Sb. (N.S.), 36(78):3 (1955),  445–478  mathnet  mathscinet  zmath 6
1951
52. S. Ya. Havinson, “On some extremal problems of the theory of analytic functions”, Uch. Zap. Mosk. Gos. Univ., 148 (1951),  133–143  mathnet  mathscinet  zmath 7
1995
53. S. V. Konyagin, S. M. Nikol'skii, S. B. Stechkin, S. Ya. Havinson, “Aleksandr L'vovich Garkavi (on his seventieth birthday)”, Uspekhi Mat. Nauk, 50:2(302) (1995),  230–231  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:2 (1995), 461–463  isi 2
1990
54. L. I. Volkovyskii, A. È. Eremenko, A. A. Kondratyuk, B. Ya. Levin, S. N. Mergelyan, I. V. Ostrovskii, S. Ya. Havinson, M. N. Sheremeta, “Anatolii Asirovich Gol'dberg (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 45:5(275) (1990),  201–203  mathnet  mathscinet; Russian Math. Surveys, 45:5 (1990), 247–250  isi

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