Eigenvalue and Eigenfunction Asymptotics for Regular Sturm-Liouville Problems

Eigenvalue Computations for Regular Matrix Sturm - Liouville Problems ∗

An algorithm is presented for computing eigenvalues of regular selfadjoint Sturm-Liouville (SL) problems with matrix coefficients and separated boundary conditions.

Eigenvalue Asymptotics for Sturm–liouville Operators with Singular Potentials

We derive eigenvalue asymptotics for Sturm–Liouville operators with singular complex-valued potentials from the space W 2 (0, 1), α ∈ [0, 1], and Dirichlet or Neumann–Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential by these two spectra.

Green’s Function for Regular Sturm-Liouville Problems

Eigenvalues of regular Sturm - Liouville problems

The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on the problem. An expression for the derivative of the n-th eigenvalue with respect to a given parameter: an endpoint, a boundary condition constant, a coefficient or weight function, is found.

Regular approximations of singular Sturm-Liouville problems

Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of ei...