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Havin Victor Petrovich

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Total publications: 54
Scientific articles: 41
Presentations: 3

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This page:4239
Abstract pages:15468
Full texts:6111
References:495
Professor
Doctor of physico-mathematical sciences (1969)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 7.03.1933
Website: http://www.math.spbu.ru/user/analysis/pers/havin.html
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.

Subject:

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.

Biography

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.

http://www.mathnet.ru/eng/person17648
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:havin.victor-p
https://mathscinet.ams.org/mathscinet/MRAuthorID/200665

Publications in Math-Net.Ru
1. Boundedness of variation of a positive harmonic function along the normals to the boundary
P. A. Mozolyako, V. P. Khavin
Algebra i Analiz, 28:3 (2016),  67–110
2. Admissible Majorants for Model Subspaces, and Arguments of Inner Functions
A. D. Baranov, V. P. Havin
Funktsional. Anal. i Prilozhen., 40:4 (2006),  3–21
3. Beurling–Malliavin multiplier theorem: the seventh proof
J. Mashreghi, F. L. Nazarov, V. P. Havin
Algebra i Analiz, 17:5 (2005),  3–68
4. Separation of singularities of analytic functions with preservation of boundedness
V. P. Khavin
Algebra i Analiz, 16:1 (2004),  293–319
5. On the I. I. Privalov theorem on the Hilbert transform of Lipschitz functions
Yu. S. Belov, V. P. Havin
Mat. Fiz. Anal. Geom., 11:4 (2004),  380–407
6. Approximation and extension problems for some classes of vector fields
S. K. Smirnov, V. P. Havin
Algebra i Analiz, 10:3 (1998),  133–162
7. Uniform approximation by harmonic differential forms. A constructive approach
E. V. Malinnikova, V. P. Havin
Algebra i Analiz, 9:6 (1997),  156–196
8. Uniform approximation by harmonic differential forms in Euclidean space
A. Presa Sagué, V. P. Havin
Algebra i Analiz, 7:6 (1995),  104–152
9. Weighted approximation for trigonometric sums and the Carleman–Krylov–Golusin formula
V. A. Bart, V. P. Havin
Zap. Nauchn. Sem. POMI, 206 (1993),  5–14
10. The uncertainty principle in harmonic analysis
B. Jöricke, V. P. Havin
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 72 (1991),  181–260
11. Poisson kernel is the only approximative identity asymptotically multiplicative on $H^\infty$
H. Wolf, V. P. Havin
Zap. Nauchn. Sem. LOMI, 170 (1989),  82–89
12. Methods and structure of commutative harmonic analysis
V. P. Havin
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 15 (1987),  6–133
13. Letter to the Editor
B. Jöricke, V. P. Havin
Zap. Nauchn. Sem. LOMI, 135 (1984),  200
14. Free interpolation and Dirichlet problem
A. O. Derviz, V. P. Havin
Zap. Nauchn. Sem. LOMI, 135 (1984),  51–65
15. Uncertainty principle for operators commuting with translations. II
B. Jöricke, V. P. Khavin
Zap. Nauchn. Sem. LOMI, 113 (1981),  97–134
16. The uncertainty principle for operators commuting with translations. I
B. Jöricke, V. P. Havin
Zap. Nauchn. Sem. LOMI, 92 (1979),  134–170
17. 2.10. The uniquness sets for analytic function with finite Dirichlet integral
V. P. Havin, S. V. Khrushchev
Zap. Nauchn. Sem. LOMI, 81 (1978),  242–245
18. 8.1. Golubev series and analyticity in a neighborhood of a continuum
V. P. Khavin
Zap. Nauchn. Sem. LOMI, 81 (1978),  33–35
19. The free interpolation in $H^\infty$ and in some other function classes. II
S. A. Vinogradov, V. P. Havin
Zap. Nauchn. Sem. LOMI, 56 (1976),  12–58
20. The solutions of the Cauchy problem for the Laplace equation (uniqueness, normality, approximation)
V. G. Maz'ya, V. P. Havin
Tr. Mosk. Mat. Obs., 30 (1974),  61–114
21. The free interpolation in $H^{\infty}$ and in some other function classes. I
S. A. Vinogradov, V. P. Havin
Zap. Nauchn. Sem. LOMI, 47 (1974),  15–54
22. The spaces $H^{\infty}$ and $L^1/H_0^1$
V. P. Havin
Zap. Nauchn. Sem. LOMI, 39 (1974),  120–148
23. Use of $(p,l)$-capacity in problems of the theory of exceptional sets
V. G. Maz'ya, V. P. Havin
Mat. Sb. (N.S.), 90(132):4 (1973),  558–591
24. Non-linear potential theory
V. G. Maz'ya, V. P. Havin
Uspekhi Mat. Nauk, 27:6(168) (1972),  67–138
25. Approximation in the mean by harmonic functions
V. G. Maz'ya, V. P. Havin
Zap. Nauchn. Sem. LOMI, 30 (1972),  91–105
26. О факторизации аналитических функций, гладких вплоть до границы
V. P. Havin
Zap. Nauchn. Sem. LOMI, 22 (1971),  202–205
27. 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
V. P. Havin
Zap. Nauchn. Sem. LOMI, 22 (1971),  161–170
28. A nonlinear analogue of the Newtonian potential, and metric properties of $(p,l)$-capacity
V. G. Maz'ya, V. P. Havin
Dokl. Akad. Nauk SSSR, 194:4 (1970),  770–773
29. Analytic functions with the boundary values having Lipschitz module
V. P. Havin, F. A. Shamoyan
Zap. Nauchn. Sem. LOMI, 19 (1970),  237–239
30. Multipliers and divisors of the Cauchy–Stiltjes type integrals
S. A. Vinogradov, M. G. Goluzina, V. P. Havin
Zap. Nauchn. Sem. LOMI, 19 (1970),  55–78
31. Approximation by analytic functions in the mean
V. P. Havin
Dokl. Akad. Nauk SSSR, 178:5 (1968),  1025–1028
32. Polynomial approximation in the mean in certain non-Carathéodory regions. II
V. P. Khavin
Izv. Vyssh. Uchebn. Zaved. Mat., 1968, no. 10,  87–94
33. Polynomial approximation in the mean in certain non Carathéodory regions. I
V. P. Khavin
Izv. Vyssh. Uchebn. Zaved. Mat., 1968, no. 9,  86–93
34. On approximation in the mean by harmonic functions
V. G. Maz'ya, V. P. Havin
Zap. Nauchn. Sem. LOMI, 5 (1967),  196–200
35. Spaces of analytic functions
V. P. Havin
Itogi Nauki. Ser. Matematika. Mat. Anal. 1964, 1966,  76–164
36. Boundary properties of integrals of Cauchy type and of conjugate harmonic functions in regions with rectifiable boundary
V. P. Havin
Mat. Sb. (N.S.), 68(110):4 (1965),  499–517
37. Analytic representation of linear functionals in spaces of harmonic and analytic functions which are continuous in a closed region
V. P. Havin
Dokl. Akad. Nauk SSSR, 151:3 (1963),  505–508
38. Some estimates of analytic capacity
V. P. Havin, S. Ya. Havinson
Dokl. Akad. Nauk SSSR, 138:4 (1961),  789–792
39. On the space of bounded regular functions
V. P. Havin
Dokl. Akad. Nauk SSSR, 131:1 (1960),  40–43
40. The separation of the singularities of analytical functions
V. P. Havin
Dokl. Akad. Nauk SSSR, 121:2 (1958),  239–242
41. Analytical continuation of power series and Faber polynomials
V. P. Havin
Dokl. Akad. Nauk SSSR, 118:5 (1958),  879–881

42. Mikhail Shlemovich Birman (obituary)
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
Uspekhi Mat. Nauk, 65:3(393) (2010),  185–190
43. Odinets Vladimir Petrovich (on his 65th birthday)
A. M. Vershik, O. Ya. Viro, V. N. Isakov, G. A. Leonov, M. J. Pratussevitch, V. P. Havin, N. A. Shirokov
Vladikavkaz. Mat. Zh., 12:4 (2010),  79–81
44. Vladimir Gilelevich Maz'ya (to his 70th brithday)
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
Uspekhi Mat. Nauk, 63:1(379) (2008),  183–189
45. Semën Yakovlevich Khavinson (obituary)
A. G. Vitushkin, A. A. Gonchar, M. V. Samokhin, V. M. Tikhomirov, P. L. Ul'yanov, V. P. Havin, V. Ya. Èiderman
Uspekhi Mat. Nauk, 59:4(358) (2004),  186–192
46. Garal'd Isidorovich Natanson (obituary)
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
Uspekhi Mat. Nauk, 59:4(358) (2004),  181–185
47. Viktor Solomonovich Videnskii (on his 80th birthday)
V. V. Zhuk, V. N. Malozemov, G. I. Natanson, V. P. Havin
Uspekhi Mat. Nauk, 57:5(347) (2002),  182–186
48. P. Koosis. The Logarithmic Integral I. Cambridge etc.: Cambridge University Press, 1988. 606 p.
V. P. Havin
Algebra i Analiz, 1:6 (1989),  235–243
49. Предисловие
N. K. Nikol'skii, V. P. Havin
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 42 (1989),  5
50. Gleb Pavlovich Akilov (obituary)
A. D. Aleksandrov, A. M. Vershik, V. V. Ivanov, A. G. Kusraev, S. S. Kutateladze, B. M. Makarov, Yu. G. Reshetnyak, V. P. Havin
Uspekhi Mat. Nauk, 43:1(259) (1988),  181–182
51. Preface
N. K. Nikol'skii, V. P. Havin
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 15 (1987),  5–6
52. Letter to the editor
S. A. Vinogradov, V. P. Havin
Zap. Nauchn. Sem. LOMI, 92 (1979),  317
53. Prefase
N. K. Nikol'skii, V. P. Khavin, S. V. Khrushchev
Zap. Nauchn. Sem. LOMI, 81 (1978),  7–9
54. Поправки к статье “О пространстве ограниченных регулярных функций” (ДАН, т. 131, № 1, 1960 г.)
V. P. Havin
Dokl. Akad. Nauk SSSR, 136:3 (1961),  520

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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