Abstract:
We study the limit behavior of sequences of cyclic systems of ordinary differential equations that were invented for the mathematical description of multistage synthesis. The main construction of the article is the distribution function of initial data. It enables us to indicate necessary and sufficient existence conditions as well as completely describe the structure and all typical properties of the limits of solutions to the integro-differential equations of “convolution” type to which the systems of cyclic synthesis are easily reduced. All notions, methods, and problems under discussion belong to such classical areas as real function theory, Euler integrals, and asymptotic analysis.
Keywords:multistage synthesis, Dirac bells, incomplete Euler gamma-function, Laplace asymptotics, Abel sums, distribution of initial data, Stieltjes integral, Helly selection principle, two-dimensional Heaviside step function, Lebesgue point, Chebyshev inequality.
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