Electron. J. Diff. Equ., Vol. 2013 (2013), No. 17, pp. 1-5.

The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter

B. J. Harris

Abstract:
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.

Submitted July 9, 2012. Published January 21, 2013.
Math Subject Classifications: 34E05.
Key Words: Sturm Liouville equation; spectral function; small eigenparameter.

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Bernie J. Harris
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115-2888, USA
email: harris@math.niu.edu

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