The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter
We study the linear second-order differential equation $$ -y'' + q(x) y = lambda y $$ where, amongst other conditions, $q in L^1[0,infty)$. We obtain a convergent series expansion for the spectral function which is valid for small values of $lambda$. We also derive an asymptotic rep...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-01-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/17/abstr.html |
| Summary: | We study the linear second-order differential equation $$ -y'' + q(x) y = lambda y $$ where, amongst other conditions, $q in L^1[0,infty)$. We obtain a convergent series expansion for the spectral function which is valid for small values of $lambda$. We also derive an asymptotic representation. |
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| ISSN: | 1072-6691 |