Geodesic
Solutions of some systems of functional equations related to complex, double, and dual numbers
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 37-46

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In this paper, we solve the problem on the embedding of three two-metric, phenomenologically symmetric geometries of two sets of rank $(3,2)$ related to complex, double, and dual numbers, into a two-metric, phenomenologically symmetric geometry of two sets of rank $(4,2)$ determined by a functions of two points $f=(x\xi +y\mu + \rho, x\eta +y\nu + \tau)$. The problem is reduced to the search for nondegeenerate solutions of three special systems of functional equations immediately related to complex, double, and dual numbers.
Keywords: functional equation, complex numbers, double numbers, dual numbers
Mots-clés : Jordan form 
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     title = {Solutions of some systems of functional equations related to complex, double, and dual numbers},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {229},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2023_229_a4/}
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V. A. Kyrov. Solutions of some systems of functional equations related to complex, double, and dual numbers. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 37-46. http://geodesic.mathdoc.fr/item/INTO_2023_229_a4/