Mathematical Notes

, Volume 104, Issue 5–6, pp 886–899 | Cite as

Semigroup Classification and Gelfand–Shilov Classification of Systems of Partial Differential Equations

  • I. V. Melnikova
  • U. A. Alekseeva


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.


semigroup of operators Fourier transform system of partial differential equations abstract Cauchy problem distribution 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Yeltsin Ural Federal UniversityEkaterinburgRussia

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