We consider the Sturm–Liouville operator perturbed by a convolution integral on finite interval with Dirichlet boundary conditions and discontinuity in middle of interval. study inverse problem recovering term from spectrum. The is reduced to solving so-called main nonlinear equation singularity. To derive this equation, we do detailed analysis kernels transformation operators for integro-diffe...

We consider finite difference approximations of solutions of inverse Sturm-Liouville problems in bounded intervals. Using three-point finite difference schemes, we discretize the equations on so-called optimal grids constructed as follows: For a staggered grid with 2k points, we ask that the finite difference operator (a k ×k Jacobi matrix) and the Sturm-Liouville differential operator share th...

Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such were obtained only one very particular situation. Here we address this gap by obtaining the case functional-differential pencils possessing more general form along nonlinear dependence on spectral parameter. For purpo...

The paper deals with the numerical solution of inverse Sturm-Liouville problems with unknown potential symmetric over the interval [0, π]. The proposed method is based on the use of a family of Boundary Value Methods, obtained as a generalization of the Numerov scheme, aimed to the computation of an approximation of the potential belonging to a suitable function space of finite dimension. The a...

Additive decompositions of a meromorphic function give rise to quotient representations of a particular form. We raise the question which quotient representations of a given function arise in this way. This question is answered by means of two characterizations via different terms. We pay particular attention to functions belonging to various subclasses of the Nevanlinna class of functions with...

We compute the asymptotics of the eigenvalues of the classical Sturm–Liouville problem with a piecewise smooth coefficient q. This means that q and/or its derivatives can have jump discontinuities. The boundary conditions are arbitrary. Our results extend the classical work of H. Hochstadt (see [Comm. Pure Appl. Math., 14 (1961), pp. 749–764]) and some related formulas discovered by G. Borg (se...