Řešitelnost grup lineárních diferenciálních operátorů n-tého řádu

Title in English Solvability of groups of linear differential operators of the n-th order
Authors

BERÁNEK Jaroslav CHVALINA Jan

Year of publication 2013
Type Article in Proceedings
Conference Acta mathematica 16, ed. PRÍRODOVEDEC, publ. č. 532
MU Faculty or unit

Faculty of Education

Citation
Field Pedagogy and education
Keywords Differential equation; solution spaces of homogeneous differential equations; solvable group.
Description The article was created on the basis of scientific research in the area of interdisciplinary relations between algebra and the theory of differential equations with the aim to find deeper connections between these two branches. In the contribution there is constructed a certain group of linear ordinary differential operators of the n-th order and there is solved the problem of its solvability. In particular, using the stabilization of the commutant chain of that group, we have obtain that the mention group is solvable. Moreover, using the one-to-one correspondence between this group and the system of solution spaces of corresponding homogeneous differential equations of the n-th order we obtain that the isomorphic group of solution spaces is also solvable.

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