Spectral Expansion on the Entire Axis of the Green Function for a Three-Layer Medium in Fundamental Functions of a Nonself-Adjoint Sturm-Liouville Operator

被引：0

作者：

Saltykov, E. G. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

DIFFERENTIAL EQUATIONS | 2008年 / 44卷 / 08期

关键词：

Green Function; Transmission Condition; Jump Discontinuity; Fundamental Function; Helmholtz Equation;

D O I：

10.1134/S0012266108080107

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a new representation of the Green function in the space R-2 for the Helmholtz equation with coefficient that is a complex-valued piecewise constant function depending on a single variable and taking three values. This representation has the form of an expansion in fundamental functions, i.e., bounded (on the entire line R-1) solutions of the Sturm-Liouville equation with a complex coefficient. The spectrum consists of two rays parallel to the real axis in the complex plane of the spectral parameter. The origin of the rays is determined by constants characterizing the coefficient in the equation.

引用

页码：1126 / 1135

页数：10