Complex WKB method for a system of two linear difference equations

Fedotov, A.

doi:10.1090/spmj/1706

Complex WKB method for a system of two linear difference equations
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by A. A. Fedotov
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 33 (2022), 405-425

DOI: https://doi.org/10.1090/spmj/1706

Published electronically: March 4, 2022

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Abstract:

Analytic solutions of the difference equation $\Psi (z+h)=M(z)\Psi (z)$ are explored. Here $z$ is a complex variable, $h>0$ is a parameter, and $M$ is a given $SL(2,\mathbb {C})$-valued function. It is assumed that $M$ either is analytic in a bounded domain or is a trigonometric polynomial. A simple method to derive the asymptotics of solutions as $h\to 0$ is described.

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