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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832565734984646656 |
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| author | Gülen Başcanbaz-Tunca |
| author_facet | Gülen Başcanbaz-Tunca |
| author_sort | Gülen Başcanbaz-Tunca |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-aa313a7c8c51447fa3e24aedb0bcb856 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aa313a7c8c51447fa3e24aedb0bcb8562025-02-03T01:06:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004271437144510.1155/S0161171204203088Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary conditionGülen Başcanbaz-Tunca0Department of Mathematics, Faculty of Science, Ankara University, Tandogan, Ankara 06100, TurkeyWe 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.http://dx.doi.org/10.1155/S0161171204203088 |
| spellingShingle | Gülen Başcanbaz-Tunca Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition International Journal of Mathematics and Mathematical Sciences |
| title | Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition |
| title_full | Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition |
| title_fullStr | Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition |
| title_full_unstemmed | Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition |
| title_short | Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition |
| title_sort | spectral properties of the klein gordon s wave equation with spectral parameter dependent boundary condition |
| url | http://dx.doi.org/10.1155/S0161171204203088 |
| work_keys_str_mv | AT gulenbascanbaztunca spectralpropertiesofthekleingordonswaveequationwithspectralparameterdependentboundarycondition |