01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
9.09.1941
E-mail:
Keywords:
asymtotic methods in analysis; theory of growth holomorphic and subharmonic functions; theory of integral equations.
Subject:
It is obtained an estimate of remainder term and uniform asymptotic expansion of integrals along curves beginning at $z_0$ that is in neighborhood of a critical point. Integrands depend on parameter. The asymptotic modulus of continuity $\omega(z,h)=|z|^{-\rho}(v(z+hz)-v(z))$ of subgarmonic function $v$ of order $\rho$ was estimated. I was introduced the class of entire functions having regular growth on the set their zeros. It was proved that such functions are divisors of entire functions of completely regular growth in the sense of Levin and Pfluger. On this basis the criterion of solvability of the free interpolation problem was founded for the class of entire functions with given indicator. It is introduced the concept of complete measure for a spread class of subgarmonic functions in the complex half-plane. For these functions complete measure play the same role as Riesz measure for subharmonic functions in whole plane. Using complete measure I and M. A. Favorov proved the version of the second main theorem for meromorphic functions in the half-plane. The question was open after work of R. Nevanlinna (1925).
Biography
Graduated from Faculty of Mathematics and Mechanics of Kharkov State University in 1963 (department of mathematical analysis). Ph.D. thesis was defended in 1970 (advisor B. Ja. Levin). D.Sci. thesis was defended in 1992. A list of my works contains mare than 20 titles. Since 1998 I and S. Ju. Favorov have led the Kharkov's seminar on the theory of functions.
Main publications:
Fedorov M. A., Grishin A. F. Some questions of the Nevanlinna theory for the complex half-plane. Kluwer Academic Publishers, Mathematical Physics, Analysis and Geometry, 1998, 1(3), 223–271.
Grishin A. F., Malyutina T. I. General properties of subharmonic functions of finite order in a complex half-plane // Вестник Харьковского национального университета. Серия Математика, прикладная математика и механика, 2000, 475(49), 20–44.
O. A. Bozhenko, A. F. Grishin, K. G. Malyutin, “An interpolation problem in the class of entire functions of zero order”, Izv. RAN. Ser. Mat., 79:2 (2015), 21–44; Izv. Math., 79:2 (2015), 233–256
A. F. Grishin, I. V. Poedintseva, “Abelian and Tauberian theorems for integrals”, Algebra i Analiz, 26:3 (2014), 1–88; St. Petersburg Math. J., 26:3 (2015), 357–409
A. F. Grishin, Nguyen Van Quynh, “Entire functions with preassigned zero proximate order”, Zap. Nauchn. Sem. POMI, 424 (2014), 141–153; J. Math. Sci. (N. Y.), 209:5 (2015), 753–760
A. F. Grishin, O. F. Krizhanovskii, “Экстремальная задача для матриц и теорема Безиковича о покрытии”, Mat. Pros., Ser. 3, 14 (2010), 196–203
2008
5.
A. Chouigui, A. F. Grishin, “A property of Azarin's limit set of subharmonic functions”, Zh. Mat. Fiz. Anal. Geom., 4:3 (2008), 346–357
6.
A. F. Grishin, A. Chouigui, “Various types of convergence of sequences of $\delta$-subharmonic functions”, Mat. Sb., 199:6 (2008), 27–48; Sb. Math., 199:6 (2008), 811–832
2005
7.
A. F. Grishin, T. I. Malyutina, “New formulas for inidicators of subharmonic functions”, Mat. Fiz. Anal. Geom., 12:1 (2005), 25–72
A. F. Grishin, I. V. Poedintseva, “Towards the Tauberian theorem of Keldysh”, Zap. Nauchn. Sem. POMI, 315 (2004), 63–89; J. Math. Sci. (N. Y.), 134:4 (2006), 2272–2287
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