Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 17, pp. 1-5.

Title: The form of the spectral function associated with Sturm-Liouville
       problems for small values of the spectral parameter
        
Author: B. J. Harris (Northern Illinois Univ., DeKalb, IL, USA)
        
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.