Havinson, Semen Yakovlevich

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Total publications: 52
Scientific articles: 50

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Doctor of physico-mathematical sciences (1962)
Birth date: 17.05.1927
Keywords: analytic functions; potential; capacities; extremal problems; approximation.


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.


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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
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
2. S. Ya. Havinson, “Approximations by wedge elements taking into account the values of the approximating elements”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, 10,  71–84  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 46:10 (2002), 69–82
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
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
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
7. S. Ya. Khavinson, “Some approximation properties of linear superpositions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, 8,  63–73  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 60–70
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
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
10. S. Ya. Khavinson, “A method for removing the multivalence of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, 11,  64–72  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:11 (1990), 80–90
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
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
13. S. Ya. Havinson, “Representation of functions of two variables by the sums $\phi(x)+\psi(y)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, 2,  66–73  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 29:2 (1985), 81–90
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. Khavinson, “19.5. The exact majorant problem”, Zap. Nauchn. Sem. LOMI, 81 (1978),  167–168  mathnet; J. Soviet Math., 26:5 (1984), 2207
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. S. Ya. Havinson, “Approximation by elements of convex sets”, Dokl. Akad. Nauk SSSR, 172:2 (1967),  294–297  mathnet  mathscinet  zmath
24. S. Ya. Havinson, “On the Rudin–Carleson theorem”, Dokl. Akad. Nauk SSSR, 165:3 (1965),  497–499  mathnet  mathscinet  zmath
25. S. Ya. Havinson, “Analytic functions of bounded type”, Itogi Nauki. Mat. Anal. 1963, 1965,  5–80  mathnet  mathscinet  zmath
26. S. Ya. Havinson, “┼xtremal 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
27. V. P. Havin, S. Ya. Havinson, “Some estimates of analytic capacity”, Dokl. Akad. Nauk SSSR, 138:4 (1961),  789–792  mathnet  mathscinet  zmath
28. S. Ya. Havinson, “Some problems concerning the completeness of systems”, Dokl. Akad. Nauk SSSR, 137:4 (1961),  793–796  mathnet  mathscinet  zmath
29. 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
30. 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
31. 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
32. 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
33. S. Ya. Havinson, “Approximation on sets of zero analytic capacity”, Dokl. Akad. Nauk SSSR, 131:1 (1960),  44–46  mathnet  mathscinet  zmath
34. S. Ya. Havinson, “On a class of extremal problems for polynomials”, Dokl. Akad. Nauk SSSR, 130:5 (1960),  997–1000  mathnet  mathscinet
35. 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, 5,  190–194  mathnet  mathscinet  zmath
36. 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
37. 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
38. 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
39. 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
40. 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
41. 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
42. 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, 3,  233–240  mathnet  mathscinet  zmath
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. 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
50. 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

51. 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
52. 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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