The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter
oleh: B. J. Harris
| Format: | Article |
|---|---|
| Diterbitkan: | Texas State University 2013-01-01 |
Deskripsi
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.