Geodesic
On the Nonlinear Operators Having Jacoby Matrix Commuting with a Ring of the Constant Matrix
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 1, pp. 108-118

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The criterion of existence of nonlinear operator $\mathbf{u}:C^m\rightarrow C^m \left(m\ge2\right)$ for which it's Jacoby matrix commutes with every constant complex matrix from any given ring $Q$ is obtained. The main theorem says that such operator exists if and only if a ring $Q$ has at least one $\left(r,l\right)$-pair.
Keywords: criterion of existence of nonlinear operator, Jacoby matrix commuting with every constant complex matrix from any given ring, $\boldsymbol{(r,l)}$-pair, Schur lemma.
Mots-clés : equivalence 
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     author = {Yu. A. Chirkunov},
     title = {On the {Nonlinear} {Operators} {Having} {Jacoby} {Matrix} {Commuting} with a {Ring} of the {Constant} {Matrix}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_1_a8/}
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Yu. A. Chirkunov. On the Nonlinear Operators Having Jacoby Matrix Commuting with a Ring of the Constant Matrix. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 1, pp. 108-118. http://geodesic.mathdoc.fr/item/VNGU_2010_10_1_a8/