Abstract
We investigate the connection between divisibility of full-rank square matrices of linear scalar differential operators over some differential field K, and the solution spaces of these matrices over the universal Picard–Vessiot extension of K. We establish some properties of the solution spaces of the greatest common right divisor and the least common left multiple of such matrices.
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ACKNOWLEDGMENTS
The authors would like to thank Michael F. Singer for his valuable advice.
Funding
Abramov’s research was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00032-a. Petkovšek’s research was supported in part by the Ministry of Education, Science, and Sport of Slovenia research program P1-0294.
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Abramov, S.A., Barkatou, M.A. & Petkovšek, M. Matrices of Scalar Differential Operators: Divisibility and Spaces of Solutions. Comput. Math. and Math. Phys. 60, 109–118 (2020). https://doi.org/10.1134/S0965542520010030
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DOI: https://doi.org/10.1134/S0965542520010030