Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition
We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y″+(λ−q(x))2y=0, x∈ℝ+=[0,∞), subject to the spectral parameter-dependent boundary condition y′(0)−(aλ+b)y(0)=0 in the space L2(ℝ+), where a≠±i, b are complex constants, q is a complex-valued funct...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204203088 |
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| Summary: | We investigate the spectrum of the differential operator
Lλ defined by the Klein-Gordon s-wave equation
y″+(λ−q(x))2y=0, x∈ℝ+=[0,∞),
subject to the spectral parameter-dependent boundary condition
y′(0)−(aλ+b)y(0)=0 in the space L2(ℝ+), where a≠±i, b are complex
constants, q is a complex-valued function. Discussing the
spectrum, we prove that Lλ has a finite number of
eigenvalues and spectral singularities with finite multiplicities
if the conditions limx→∞q(x)=0, supx∈R+{exp(ϵx)|q′(x)|}<∞,
ϵ>0, hold. Finally we show the properties of the
principal functions corresponding to the spectral singularities. |
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| ISSN: | 0161-1712 1687-0425 |