Asymptotics of eigenvalues of a singular differential operator of Jacobi type (Q5932077)

Let \(T\) be the differential operator \[ Ty=(1-x^2)y''+[\beta-\alpha -(\alpha+\beta+2)x]y' \] on the segment \([-1,1]\), with \(y\), \(Ty\in L_2^w(-1,1)\), and the weight \(w(x)=(1-x)^{\alpha}(1+x)^\beta\), \(\alpha\), \(\beta\in \mathbb{R}\), \(\alpha\), \(\beta>-1\). Denote \(P\) the operator of multiplication by the function \(p(x)\) which is twice continuously differentiable on \((a,b)\). The authors investigate the asymptotic behaviour of the eigenvalues of the operator \(T+P\).