Semigroup Classification and Gelfand–Shilov Classification of Systems of Partial Differential Equations
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Two approaches to systems of linear partial differential equations are considered: the traditional approach based on the generalized Fourier transform and the semigroup approach, under which the system is considered as a particular case of an operator-differential equation. For these systems, the semigroup classification and the Gelfand–Shilov classification are compared.
Keywordssemigroup of operators Fourier transform system of partial differential equations abstract Cauchy problem distribution
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