Complex WKB method for a system of two linear difference equations

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-03-04 DOI:10.1090/spmj/1706

A. Fedotov

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引用次数: 0

Abstract

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

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两个线性差分方程组的复WKB方法

探讨了差分方程Ψ（z+h）=M（z）Ψ。这里z z是复变量，h＞0 h＞0是参数，M M是给定的SL（2，C）SL（2、\mathbb｛C｝）值函数。假设M M在有界域中是解析的，或者是三角多项式。导出解的渐近性为h的一种简单方法→ 0 h\到0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.