In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high frequency component may sign...

In this paper, we deal with the inverse spectral problem for the equation −(pu′)′ +qu = λru on a finite interval (0, h). The above equation subjected to appropriate boundary conditions on zero and h gives the vibrations of a string of length h. Using the Dirichlet-to-Neumann map type approach known in the multidimensional Calderón problem, we prove some uniqueness results of one or two disconti...

We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the S...

We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.

In this paper, we consider the inverse nodal problem for a quadratic pencil of Sturm$-$Liouville equations with parameter-dependent Bitsadze$-$Samarskii type nonlocal boundary condition and give an algorithm reconstruction potential functions by obtaining asymptotics points.

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In this study by modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we investigate some spectral properties of one Sturm-Liouville type problem on two disjoint intervals.

For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2 ∈ R and if u1,2 solve the differential equation Huj = Ejuj , j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E1,E2)(H) of H equals the number of zeros of the Wronskian of u1 and u2.