As is known, beginning in the fundamental papers by E. Hille, R. Phillips, and other authors, an important place in the theory of equations of parabolic type is occupied by one-parameter semigroups of linear transformations U(t), T ≥ 0, said to be canonical and determined by the relation U(α ? β) = U(α)U(β), where α and β are real or complex numbers [8, p. 275 of the Russian translation]. In the system of numbers under consideration, there is a subset determining semigroups corresponding to various addition operations.
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