Elliptic eigenvalue problems with an indefinite weight function (Q5906714)

The author studies elliptic eigenvalue problems with weight function; i.e., the problems \(Lu=\lambda g(x)u\) \((x\in G\subset\mathbb R^n)\) and \(B_ju|_\Gamma =0\) \((j=1,\dots ,m)\), where \(L\) is a selfadjoint (in \(L_2(G)\)) elliptic operator, \(g(x)\) is a measurable function changing sign in \(G\), and \(\{ B_j\}\) is a collection of boundary operators. The author studies whether eigenfuctions and associated functions of this problem possess the unconditional basis property in the space \(L_2\) with weight \(|g|\).