Spectral theory of operators is one of the important directions of functional analysis. The spectral theory of operator pencils is raised as the result of study of the problems of ordinary differential equations with the boundary conditions. But the multiparameter spectral theory is raised in the result of the study of the problems of the partial differential equations and the equations of the mathematical physics.The physical sciences open more and more challenges for mathematicians. In particular, the research of the problems associated with the physical processes and, consequently, the study of partial differential equations and mathematical physics equations, required a new approach. The method of separation of variables in many cases turned out to be the only acceptable, since it reduces finding a solution to a complex equation with many variables to find a solution to a system of ordinary differential equations, which are much easier to study. For example, a multivariable problems cause problems in quantum mechanics, diffraction theory, the theory of elastic shells, nuclear reactor calculations , stochastic diffusion processes, Brownian motion, boundary value problems for equations of elliptic-parabolic type, the Cauchy problem for ultraparabolic equations and etc.

Despite the urgency and prescription studies, spectral theory of multiparameter systems studied was not enough. The available results in this area until recently only dealt with seltadjoint multiparameter systems. Original research papers in this area will help further explored this actual direction of functional analysis.

It is expected to pay more attention to the study of the particular case of nonlinear multiparameter systems of operators in the Hilbert space, namely, to the operator pencils and nonlinear algebraic systems with many variables.

Aims and Scope:

1. Spectral problem of multiparameter system
2. Operator pencils in Hilbert space.
3. Problem of completeness of eigen and associated vectors of multiparameter systems of operator pencils in Hilbert spaces.
4. Nonlinear algebraic equations with many variables.
5. Bases of eigen and associated vectors of multiparameter system.
6. Application of results of multiparameter spectral theory.
7. Fundamental notions of spectral theory of operators.