Fedotov, A. A.; Shchetka, E. V. The complex WKB method for difference equations in bounded domains. (English. Russian original) Zbl 1476.39025 J. Math. Sci., New York 224, No. 1, 157-169 (2017); translation from Zap. Nauchn. Semin. POMI 438, 236-256 (2015). Summary: The difference Schrödinger equation \(\psi(z+h)+\psi(z-h)+v(z)\psi(z) = E\psi(z)\), \(z\in\mathbb{C}\), is considered, where \(h > 0\) and \(E\in\mathbb{C}\) are parameters and \(v\) is a function analytic in a bounded domain \(D\subset \mathbb{C}\). An asymptotic method is developed for studying its solutions in the domain \(D\) for small positive \(h\). Cited in 8 Documents MSC: 39A70 Difference operators 34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations 39A12 Discrete version of topics in analysis 39B32 Functional equations for complex functions Keywords:difference Schrödinger equation; complex WKB method; asymptotic method PDFBibTeX XMLCite \textit{A. A. Fedotov} and \textit{E. V. Shchetka}, J. Math. Sci., New York 224, No. 1, 157--169 (2017; Zbl 1476.39025); translation from Zap. Nauchn. Semin. POMI 438, 236--256 (2015) Full Text: DOI References: [1] V. Buslaev and A. Fedotov, “The complex WKB method for the Harper equation,” Algebra Analiz, 6, No. 3, 59-83 (1994). · Zbl 0839.34066 [2] M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations [in Russian], Librokom, Moscow (2009). [3] A. Fedotov and F. Klopp, “A complex WKB method for adiabatic problems,” Asymptotic Analysis, 27, 219-264 (2001). · Zbl 1001.34082 [4] A. A. Fedotov, “The method of monodromization in the theory of quasiperiodic equations,” Algebra Analiz, 25, No. 2, 203-235 (2013). · Zbl 1001.34082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.