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- Title
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.
- Authors
Saltykov, E.
- Abstract
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.
- Subjects
HELMHOLTZ equation; MATHEMATICAL variables; SPECTRUM analysis; RAYS (Graph theory); FOURIER series
- Publication
Differential Equations, 2008, Vol 44, Issue 8, p1126
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266108080107