Inverse spectral theory for some singular Sturm-Liouville problems (Q1313493)

The objects of investigation are operators defined by means of differential forms \(D^ 2 + p(x) + m(m+1)/x^{-2}\) and boundary conditions \(f(+0) = 0\), \(f'(1) + bf(1) = 0\) (the case \(b = \infty\) is considered, too). The boundary value problem for the Helmholtz equation with spherical symmetric coefficient can be reduced to a sequence of problems for such operators. The main results consist in theorems which characterize spectral properties of the operators and isospectral sets (the sets of coefficients \(p(x)\) which define the same spectrum).