We present a direct and rather elementary method for defining and analyzing one-dimensional Schrödinger operators H = −d2/dx2 + μ with measures as potentials. The basic idea is to let the (suitably interpreted) equation −f ′′+μf = zf take center stage. We show that the basic results from direct and inverse spectral theory then carry over to Schrödinger operators with measures.

We utilize the theory of de Branges spaces to show when certain Schrödinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness theorem for perturbed spherical Schrödinger operators.

In this paper the inverse eigenvalue problem of recovering the real coefficients in a Sturm–Liouville problem with nonselfadjoint boundary conditions depending on the spectral parameter from the eigenvalues is solved using entire-function theory and the solution of a Marchenko integral equation.

We show that the finite Toda lattice with complex-valued initial data can be integrated by the inverse spectral method. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem from the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the soluti...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.

In this work we outline the general analytic characteristics satisfied by scalar correlation functions at finite temperature in local quantum field theory. We demonstrate that locality of fields particular imposes significant constraints on spectral structure theory, and enables non-perturbative effects experienced thermal particle states to be directly calculated from Euclidean functions, avoi...