Speciality:
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).
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.
