Sturm-Liouville operator
= Sturm-Liouville operator
{c}
{title2=$L\xi=W^{-1}[-(P\xi\prime)\prime+Q\xi]$}
The weighted operator $L=W^{-1}[-(P\xi\prime)\prime+Q\xi]$, with real coefficients and $P,W>0$ in the interior, defines a <Sturm-Liouville problem>. Its realization as a <self-adjoint differential operator> requires a domain whose endpoint conditions annihilate the boundary form $[P(\eta\prime^*\xi-\eta^*\xi\prime)]$. Its <Rayleigh quotient> uses the weight $W$ in the denominator.