Geodesic
Normalized form and resonances of matrix-valued functions of two variables
Problemy fiziki, matematiki i tehniki, no. 4 (2017), pp. 33-39

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Matrix-functions that arise when solving systems of differential equations with Delta-shaped coefficients are investigated. The process of reducing the matrix-function $F(\mu,\varepsilon)$ is considered depending on two variables to the normal form by means of the matrix functions G and T such that their elements belong to a ring wide then the ring containing elements of $F(\mu,\varepsilon)$. The explicit form of the main term of expansion $[F(\mu,\varepsilon)]^{-1}$ in the case of matrices of dimension $2$ is found explicitly. The cases of resonance for systems with delta-coefficients are revealed.
Keywords: matrix-function, normalized form, resonance, ring, main term of expansion. 
@article{PFMT_2017_4_a5,
     author = {A. B. Antonevich and M. G. Kot},
     title = {Normalized form and resonances of matrix-valued functions of two variables},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {33--39},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_4_a5/}
}
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A. B. Antonevich; M. G. Kot. Normalized form and resonances of matrix-valued functions of two variables. Problemy fiziki, matematiki i tehniki, no. 4 (2017), pp. 33-39. http://geodesic.mathdoc.fr/item/PFMT_2017_4_a5/