01.01.02 (Differential equations, dynamical systems, and optimal control)
integral and integral-differencial equations; functional analysis (factorization of operators etc.); mathematical physics (radiative transfer, kinetic theory of gases etc.); stochastic processes; multidimensional complex analysis; astrophysics.
The theory of nonlinear factorization equations (NFE) of integral and other linear operators was founded, including various applications. Generalized Volterian factorization problem for non-invertible integral operators was formulated and solved. A complete theory of Wiener–Hopf scalar and vector integral equations for conservative and supercritical (singular) cases was developed, using NFE. A theory of generalized Ambartsumian equation and Riccati-type operator equation was developed. A principal new approach to the solution of convolution-type integral equations on a finite interval was developed, including applications in radiative transfer (RT) theory. A structural theory for renewal equations (on the half-line and on the whole line) and Markov renewal equations was developed, including new-type limit and asymptotic theorems. For the first time the theory and solution methods for RT problems in spectral lines in general laws of non-coherent scattering, as well as - the mathematical theory of anisotrope scattering with summable indicatrix (including solution of Miln problem) was developed. The method of self-consisting optical depths (coming from Edington and V. Ambartsumian ideas) for exact solution of non-linear RT problems, was developed. Some factorization and other, methods to efficient numerical-analytical solution of RT problems and problems of kinetic theory of gases, was developed. The domains of normal convergence of multidimensional Loran series was constructed.
Graduated from Faculty of Mathematics and Mechanics of Yerevan State University in 1963 (department of math. analysis and theory of functions). Was Lenin scholarship holder. Ph. D. thesis was defended in 1968. D. Sci. thesis was defended in 1979. A list of my works contains more than 130nbsp;titles. Since 1971 I have led the research seminar on integral equations and mathematical physics; 35 years of teaching experience at Yerevan State University and other high schools; was head of some math. chairs; supervision of 16 Ph. D. and 5 D. Sci. thesis.
Member of a number local and international Scientific Boards.
Engibaryan N. B., “Uravneniya v svertkakh, soderzhaschie singulyarnye veroyatnostnye raspredeleniya”, Izv. RAN, ser. matem., 60:2 (1996), 21–48