Havin, Victor Petrovich

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Total publications: 55
Scientific articles: 42
Presentations: 3

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Doctor of physico-mathematical sciences (1969)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 7.03.1933
Keywords: spaces of analytic functions; Cauchy type integrals; separation of singularities of analytic functions; Taylor coefficients of various classes of analytic functions; Hardy classes; inner-outer factorization of analytic functions; approximation by rational, analytic and harmonic functions; analytic capacity; non linear potential theory; the Cauchy problem for the Laplace operator; harmonic fields and differential forms; uncertainty principle in Fourier analysis; coinvariant (model) subspaces of the Hardy space.


A solution of Golubev"s problem was given on Laurent generalized representation of an arbitrary function analytic in the complement of a simple rectifiable arc. A new approach to separation of singularities of analytic functions (the Poincare–Aronszajn theorem) was found. Conditions were found ensuring the separation of singularities preserving the uniform boundedness (joint work with A. Nersessyan). For some classes of functions analytic in a disc the invariance under division by an inner function is proved. The phenomenon of the twofold decrease of smoothness of an analytic function compared with the smoothness of its modulus on the boundary is studied ; "the smoothness" can be understood in various senses. Integral analogs of the Vitushkin theorem on the uniform rational approximation were obtained; in the mean square case the role of analytic capacity is played by the classical logarithmic capacity. In a series of joint publications with V. G. Maz'ya "the nonlinear potrential theory" was founded and applied to problems of uniqueness and approximation for analytic and harmonic functions. Some problems posed by S. N. Mergelyan were solved on the solutions of the Cauchy problem for the Laplace equation. (Some rather complete results on "the free solvability" of the Cauchy problem for harmonic functions of two varables were obtained in a joint work with J. Bourgain, A. Aleksandrov, M. Giesecke, and Yu. Vymenets). In a joint work with B. Joericke free interpolation by harmonic functions (in the spirit of Carleson–Garnett) was studied when the interpolation data are defined on a subset of the closed domain and on a part of the boudary. In a series of joint works with B. Joericke some "uncertainty principles" were proved for the convolution integral operators. A monograph (by V. Havin and B. Joericke) is devoted to the uncertainty principle in Fourier analysis ("a non zero function and its Fourier image cannot be too small simultaneously"). In a series of joint works with A. Presa, Ye. Malinnikova, and S. Smirnov approximation properties of harmonic vector fields and differential forms were studied; multidimensional analogs of the Runge theorem and Hartogs–Rosental theorem were proved, and it was shown that the analog of Bishop's localization principle is not valid in dimensions higher than two. In a joint work with J. Mashreghi some "multiplier theorems" (in the spirit of Beurling–Malliavin) for "model subspaces" (i.e. inverse shift invariant) of the Hardy space were obtained. An uncertainty principle for M. Riesz potentials on the line was found; its sharpness was proved in a joint work with D. Belyaev.


Graduated from department of mathematics and mechanics of Leningrad State University. Ph.D. thesis was defended in 1958. D.Sci. thesis was defended in 1969. The list of my works contains 100 titles (appr.) including one monograph and three textbooks. Since 1963 I lead a joint seminar of Steklov Institute and St. Petersburg State University on function operator theory (until 1991 we led the seminar with N. K. Nikolskii). 26 Ph.D. theses were written under my supervision; 8 of my former Ph.D. students are now doctors of sciences, and three of them are the Salem Prize winners (the Prize was founded by the Paris Academy).

I lectured and held visiting positions in many universities and mathematical institutes of the former USSR (Moscow, Kharkov, Rostov, Yerevan, Vladivostok, Novosibirsk, Tashkent, Vilnyus), in Cuba (Oriente), and also in many universities abroad (Sweden, Denmark, Finland, Germany, Chech Republic, Poland, USA, Canada, Spain, Norway, France, Israel). I taught 7 semesters at McGill university (Montreal). I took part in many conferences. In 1993 I got a Ph.D. degree honoris causa at Linkoping University (Sweden) and became the Onsager Professor-2000 at Trondheim University (Norway). In 1996 I gave a Spencer lecture at the Kansas State University. I also got awards of Ministery of Education of Russian Federation and of St. Petersburg State University.

Main publications:
  • Havin V. Golubev series and analyticity on a continuum // Lecture Notes in Math., 1984, 1043, 670–673.
  • Havin V., Joericke B. The Uncertainty Principle in Harmonic Analysis. Springer-Verlag, 1994.
  • Khavin V. P., Smirnov S. K. Approximation and extension problems for some classes of vector fields // St. Petersburg Math. J., 1999, 10(3), 507–528.
  • Beliaev D. B., Havin V. P. On the uncertainty principle for M. Riesz potentials // Arkiv for Mat., 2001, 39(2), 223–243.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. P. A. Mozolyako, V. P. Khavin, “Boundedness of variation of a positive harmonic function along the normals to the boundary”, Algebra i Analiz, 28:3 (2016),  67–110  mathnet  mathscinet  elib; St. Petersburg Math. J., 28:3 (2017), 345–375  isi  scopus
2. A. D. Baranov, V. P. Havin, “Admissible Majorants for Model Subspaces, and Arguments of Inner Functions”, Funktsional. Anal. i Prilozhen., 40:4 (2006),  3–21  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:4 (2006), 249–263  isi  scopus
3. J. Mashreghi, F. L. Nazarov, V. P. Havin, “Beurling–Malliavin multiplier theorem: the seventh proof”, Algebra i Analiz, 17:5 (2005),  3–68  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 17:5 (2006), 699–744
4. V. P. Khavin, “Separation of singularities of analytic functions with preservation of boundedness”, Algebra i Analiz, 16:1 (2004),  293–319  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:1 (2005), 259–283
5. Yu. S. Belov, V. P. Havin, “On the I. I. Privalov theorem on the Hilbert transform of Lipschitz functions”, Mat. Fiz. Anal. Geom., 11:4 (2004),  380–407  mathnet  mathscinet  zmath
6. S. K. Smirnov, V. P. Havin, “Approximation and extension problems for some classes of vector fields”, Algebra i Analiz, 10:3 (1998),  133–162  mathnet  mathscinet  zmath; St. Petersburg Math. J., 10:3 (1999), 507–528
7. E. V. Malinnikova, V. P. Havin, “Uniform approximation by harmonic differential forms. A constructive approach”, Algebra i Analiz, 9:6 (1997),  156–196  mathnet  mathscinet  zmath; St. Petersburg Math. J., 9:6 (1998), 1149–1180
8. A. Presa Sagué, V. P. Havin, “Uniform approximation by harmonic differential forms in Euclidean space”, Algebra i Analiz, 7:6 (1995),  104–152  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:6 (1996), 943–977
9. V. A. Bart, V. P. Havin, “Weighted approximation for trigonometric sums and the Carleman–Krylov–Golusin formula”, Zap. Nauchn. Sem. POMI, 206 (1993),  5–14  mathnet  mathscinet  zmath; J. Math. Sci., 80:4 (1996), 1873–1879
10. B. Jöricke, V. P. Havin, “The uncertainty principle in harmonic analysis”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 72 (1991),  181–260  mathnet  mathscinet  zmath
11. H. Wolf, V. P. Havin, “Poisson kernel is the only approximative identity asymptotically multiplicative on $H^\infty$”, Zap. Nauchn. Sem. LOMI, 170 (1989),  82–89  mathnet  mathscinet  zmath; J. Soviet Math., 63:2 (1993), 159–163
12. V. P. Havin, “Methods and structure of commutative harmonic analysis”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 15 (1987),  6–133  mathnet  mathscinet  zmath
13. B. Jöricke, V. P. Havin, “Letter to the Editor”, Zap. Nauchn. Sem. LOMI, 135 (1984),  200  mathnet
14. A. O. Derviz, V. P. Havin, “Free interpolation and Dirichlet problem”, Zap. Nauchn. Sem. LOMI, 135 (1984),  51–65  mathnet  mathscinet  zmath
15. V. P. Havin, “The uncertaincy principle for one-dimensional M. Riesz potentials”, Dokl. Akad. Nauk SSSR, 264:3 (1982),  559–563  mathnet  mathscinet  zmath
16. B. Jöricke, V. P. Khavin, “Uncertainty principle for operators commuting with translations. II”, Zap. Nauchn. Sem. LOMI, 113 (1981),  97–134  mathnet  mathscinet  zmath; J. Soviet Math., 22:6 (1983), 1758–1783
17. B. Jöricke, V. P. Havin, “The uncertainty principle for operators commuting with translations. I”, Zap. Nauchn. Sem. LOMI, 92 (1979),  134–170  mathnet  mathscinet  zmath
18. V. P. Havin, S. V. Khrushchev, “2.10. The uniquness sets for analytic function with finite Dirichlet integral”, Zap. Nauchn. Sem. LOMI, 81 (1978),  242–245  mathnet; J. Soviet Math., 26:5 (1984), 2265–2267
19. V. P. Khavin, “8.1. Golubev series and analyticity in a neighborhood of a continuum”, Zap. Nauchn. Sem. LOMI, 81 (1978),  33–35  mathnet; J. Soviet Math., 26:5 (1984), 2107–2108
20. S. A. Vinogradov, V. P. Havin, “The free interpolation in $H^\infty$ and in some other function classes. II”, Zap. Nauchn. Sem. LOMI, 56 (1976),  12–58  mathnet  mathscinet  zmath; J. Soviet Math., 14:2 (1980), 1027–1065
21. V. G. Maz'ya, V. P. Havin, “The solutions of the Cauchy problem for the Laplace equation (uniqueness, normality, approximation)”, Tr. Mosk. Mat. Obs., 30 (1974),  61–114  mathnet  mathscinet  zmath
22. S. A. Vinogradov, V. P. Havin, “The free interpolation in $H^{\infty}$ and in some other function classes. I”, Zap. Nauchn. Sem. LOMI, 47 (1974),  15–54  mathnet  mathscinet  zmath
23. V. P. Havin, “The spaces $H^{\infty}$ and $L^1/H_0^1$”, Zap. Nauchn. Sem. LOMI, 39 (1974),  120–148  mathnet  mathscinet  zmath
24. V. G. Maz'ya, V. P. Havin, “Use of $(p,l)$-capacity in problems of the theory of exceptional sets”, Mat. Sb. (N.S.), 90(132):4 (1973),  558–591  mathnet  mathscinet  zmath; Math. USSR-Sb., 19:4 (1973), 547–580
25. V. G. Maz'ya, V. P. Havin, “Non-linear potential theory”, Uspekhi Mat. Nauk, 27:6(168) (1972),  67–138  mathnet  mathscinet  zmath; Russian Math. Surveys, 27:6 (1972), 71–148
26. V. G. Maz'ya, V. P. Havin, “Approximation in the mean by harmonic functions”, Zap. Nauchn. Sem. LOMI, 30 (1972),  91–105  mathnet  mathscinet  zmath
27. V. P. Havin, “О факторизации аналитических функций, гладких вплоть до границы”, Zap. Nauchn. Sem. LOMI, 22 (1971),  202–205  mathnet  zmath
28. V. P. Havin, “Impossibility of the Carleman approximation of function continuous on the unit circumference by boundary values of functions analytic and uniformly continuous in the unit disc”, Zap. Nauchn. Sem. LOMI, 22 (1971),  161–170  mathnet  mathscinet  zmath
29. V. G. Maz'ya, V. P. Havin, “A nonlinear analogue of the Newtonian potential, and metric properties of $(p,l)$-capacity”, Dokl. Akad. Nauk SSSR, 194:4 (1970),  770–773  mathnet  mathscinet  zmath
30. V. P. Havin, F. A. Shamoyan, “Analytic functions with the boundary values having Lipschitz module”, Zap. Nauchn. Sem. LOMI, 19 (1970),  237–239  mathnet  mathscinet  zmath
31. S. A. Vinogradov, M. G. Goluzina, V. P. Havin, “Multipliers and divisors of the Cauchy–Stiltjes type integrals”, Zap. Nauchn. Sem. LOMI, 19 (1970),  55–78  mathnet  mathscinet  zmath
32. V. P. Havin, “Approximation by analytic functions in the mean”, Dokl. Akad. Nauk SSSR, 178:5 (1968),  1025–1028  mathnet  mathscinet  zmath
33. V. P. Khavin, “Polynomial approximation in the mean in certain non-Carathéodory regions. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, 10,  87–94  mathnet  mathscinet  zmath
34. V. P. Khavin, “Polynomial approximation in the mean in certain non Carathéodory regions. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, 9,  86–93  mathnet  mathscinet  zmath
35. V. G. Maz'ya, V. P. Havin, “On approximation in the mean by harmonic functions”, Zap. Nauchn. Sem. LOMI, 5 (1967),  196–200  mathnet  mathscinet  zmath
36. V. P. Havin, “Spaces of analytic functions”, Itogi Nauki. Ser. Matematika. Mat. Anal. 1964, 1966,  76–164  mathnet  mathscinet
37. V. P. Havin, “Boundary properties of integrals of Cauchy type and of conjugate harmonic functions in regions with rectifiable boundary”, Mat. Sb. (N.S.), 68(110):4 (1965),  499–517  mathnet  mathscinet  zmath
38. V. P. Havin, “Analytic representation of linear functionals in spaces of harmonic and analytic functions which are continuous in a closed region”, Dokl. Akad. Nauk SSSR, 151:3 (1963),  505–508  mathnet  mathscinet  zmath
39. V. P. Havin, S. Ya. Havinson, “Some estimates of analytic capacity”, Dokl. Akad. Nauk SSSR, 138:4 (1961),  789–792  mathnet  mathscinet  zmath
40. V. P. Havin, “On the space of bounded regular functions”, Dokl. Akad. Nauk SSSR, 131:1 (1960),  40–43  mathnet  mathscinet  zmath
41. V. P. Havin, “The separation of the singularities of analytical functions”, Dokl. Akad. Nauk SSSR, 121:2 (1958),  239–242  mathnet  mathscinet  zmath
42. V. P. Havin, “Analytical continuation of power series and Faber polynomials”, Dokl. Akad. Nauk SSSR, 118:5 (1958),  879–881  mathnet  mathscinet  zmath

43. V. M. Babich, V. S. Buslaev, A. M. Vershik, S. G. Gindikin, S. V. Kislyakov, A. A. Laptev, V. A. Marchenko, N. K. Nikol'skii, L. A. Pastur, B. A. Plamenevskii, M. Z. Solomyak, T. A. Suslina, N. N. Ural'tseva, L. D. Faddeev, V. P. Khavin, D. R. Yafaev, “Mikhail Shlemovich Birman (obituary)”, Uspekhi Mat. Nauk, 65:3(393) (2010),  185–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 65:3 (2010), 569–575  isi
44. A. M. Vershik, O. Ya. Viro, V. N. Isakov, G. A. Leonov, M. J. Pratussevitch, V. P. Havin, N. A. Shirokov, “Odinets Vladimir Petrovich (on his 65th birthday)”, Vladikavkaz. Mat. Zh., 12:4 (2010),  79–81  mathnet
45. M. S. Agranovich, Yu. D. Burago, B. R. Vainberg, M. I. Vishik, S. G. Gindikin, V. A. Kondrat'ev, V. P. Maslov, S. V. Poborchi, Yu. G. Reshetnyak, V. P. Khavin, M. A. Shubin, “Vladimir Gilelevich Maz'ya (to his 70th brithday)”, Uspekhi Mat. Nauk, 63:1(379) (2008),  183–189  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:1 (2008), 189–196  isi
46. 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
47. V. M. Babich, A. M. Vershik, V. S. Videnskii, O. L. Vinogradov, I. K. Daugavet, N. Yu. Dodonov, V. V. Zhuk, B. M. Makarov, A. N. Podkorutov, Yu. G. Reshetnyak, M. A. Skopina, V. L. Fainshmidt, V. P. Havin, N. A. Shirokov, “Garal'd Isidorovich Natanson (obituary)”, Uspekhi Mat. Nauk, 59:4(358) (2004),  181–185  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:4 (2004), 771–776  isi
48. V. V. Zhuk, V. N. Malozemov, G. I. Natanson, V. P. Havin, “Viktor Solomonovich Videnskii (on his 80th birthday)”, Uspekhi Mat. Nauk, 57:5(347) (2002),  182–186  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:5 (2002), 1033–1038  isi
49. V. P. Havin, “P. Koosis. The Logarithmic Integral I. Cambridge etc.: Cambridge University Press, 1988. 606 p.”, Algebra i Analiz, 1:6 (1989),  235–243  mathnet  mathscinet  zmath
50. N. K. Nikol'skii, V. P. Havin, “Предисловие”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 42 (1989),  5  mathnet
51. A. D. Aleksandrov, A. M. Vershik, V. V. Ivanov, A. G. Kusraev, S. S. Kutateladze, B. M. Makarov, Yu. G. Reshetnyak, V. P. Havin, “Gleb Pavlovich Akilov (obituary)”, Uspekhi Mat. Nauk, 43:1(259) (1988),  181–182  mathnet  mathscinet; Russian Math. Surveys, 43:1 (1988), 221–223  isi
52. N. K. Nikol'skii, V. P. Havin, “Preface”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 15 (1987),  5–6  mathnet
53. S. A. Vinogradov, V. P. Havin, “Letter to the editor”, Zap. Nauchn. Sem. LOMI, 92 (1979),  317  mathnet  mathscinet
54. N. K. Nikol'skii, V. P. Khavin, S. V. Khrushchev, “Prefase”, Zap. Nauchn. Sem. LOMI, 81 (1978),  7–9  mathnet; J. Soviet Math., 26:5 (1984), I–II
55. V. P. Havin, “Поправки к статье “О пространстве ограниченных регулярных функций” (ДАН, т. 131, № 1, 1960 г.)”, Dokl. Akad. Nauk SSSR, 136:3 (1961),  520  mathnet

Presentations in Math-Net.Ru
1. Об усиленной сходимости аппроксимативных единиц
V. P. Khavin, P. A. Mozolyako
Seminar on Operator Theory and Function Theory
November 22, 2010 17:30
2. Воспоминания о Владимире Ивановиче Смирнове
V. P. Havin
At St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
May 19, 2008   
3. On the interpolation Goluzin–Krylov formula
V. P. Havin
Meetings of the St. Petersburg Mathematical Society
March 14, 2006

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