Abstract
The eigenvalue problem of finitedimensional transformations is very relevant in the economy, especially when a pandemic appears due to the spread of coronavirus and economic disasters. The authors propose an interpretation of the economic meaning of this task – the task of finding eigenvalues and eigenvectors of finitedimensional transformations. The existence of a certain set of valid eigenfunctions means that the eco–system is involved in the process of selfregulation: such a system is capable of producing an effect in the form of a vector collinear to the exogenous effect of this stimulus when a stimulus acts on it. If there are no such significant strategies, then every external influence will be functionally distorted by the system operator. An unpredictable reaction, aggravated by the dynamics of the eco–system, increases the investment risks inherent in it: it is actively exposed either to the risk of stagnation, or an unpredictable increase in the number of risky projects awaits it. By choosing, if possible, their own states, the researcher thereby reduces the risk function and increases the stability barrier of the normal functioning of the ecosystem. In this paper, from an economic point of view, the problems of proper numbers and eigenfunctions of the Fredholm integral operator, the differential operator "velocity", its square, the differential operator "acceleration", as well as pseudodifferential operators that play an important role in nonlinear models of economics are considered.
Published Version
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