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 Mat. Zametki, 2018, Volume 104, Issue 6, Pages 895–911 (Mi mz11547)

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

I. V. Mel'nikova, U. A. Alekseeva

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: 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.

Keywords: semigroup of operators, Fourier transform, system of partial differential equations, abstract Cauchy problem, distribution.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 02.À03.21.0006 This work was supported by Regulation no. 211 of the Government of the Russian Federation (contract no. 02.A03.21.0006).

DOI: https://doi.org/10.4213/mzm11547

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English version:
Mathematical Notes, 2018, 104:6, 886–899

Bibliographic databases:

Document Type: Article
UDC: 517.983+517.982.4+517.95
Revised: 30.12.2017

Citation: I. V. Mel'nikova, U. A. Alekseeva, “Semigroup Classification and Gelfand–Shilov Classification of Systems of Partial Differential Equations”, Mat. Zametki, 104:6 (2018), 895–911; Math. Notes, 104:6 (2018), 886–899

Citation in format AMSBIB
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