Geodesic
Solution of a $\mathbb R$-Linear Conjugation Problem for a Parallel-Layered Medium in the Class of Piecewise Meromorphic Functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 145-157

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The problem of $\mathbb R$-linear conjugation for parallel-layered $(n+1)$-phase media is solved in the class of piecewise meromorphic functions with given principal parts. The solution is written as a left-sided Fourier integral with a known original. In addition, some sufficient conditions under which the Fourier integral can be represented as an absolutely convergent series are obtained.
Keywords: parallel-layered media, $\mathbb R$-linear conjugation problem, heterogeneous structures, Milne-Thomson theorem, piecewise meromorphic functions. 
@article{UZKU_2012_154_3_a13,
     author = {A. Yu. Kazarin},
     title = {Solution of a $\mathbb R${-Linear} {Conjugation} {Problem} for a {Parallel-Layered} {Medium} in the {Class} of {Piecewise} {Meromorphic} {Functions}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {145--157},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a13/}
}
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A. Yu. Kazarin. Solution of a $\mathbb R$-Linear Conjugation Problem for a Parallel-Layered Medium in the Class of Piecewise Meromorphic Functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 145-157. http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a13/